I taught for years and 1000's of hours
I have to be honest as a CFI, I never taught my students what side to offset when going around from a balked landing due to plane on the runway. I taught balked landings from 500 feet to 5 feet but in general the plan was to fly the plane straight most of the time.
If I have to deviate away from the plane on the runway, I would turn in the direction to the degree that gave me most clearance from people and obstacles as safely as possible. As PIC I can make any turn I want including 180 if that is prudent. A 180 might be prudent into a one way mountain strip? Bull by the horns.
"protected (pattern-side) side which would enable an early cross-wind turn and minimizes crossing flight path potential. The AIM says to pass on the right but that has potential risks if departing traffic is straight out, and you need to turn left cross-wind. What's the consensus?"
I'm not sure about what AIM/FAR reference you are quoting, about passing to the right? Do you have section, par number? Below I cut-n-pasted FAR 91.113 - Right-of-way. Landing planes on short final have right of way, period. The RIGHT turn or right side rule is planes approaching HEAD ON. There is an "overtaking" rule par (f), but again this is inflight, nothing to do with overflying a plane on the runway during a Balked landing. Also separation rule (91.119 - Minimum safe altitudes) do not apply when landing. So you can fly right over the plane on the runway. There is no "airplane cut me off on short final" rule. It's really an Oh shoot moment, but fly the plane first.
Here is the FAR's I think apply
Sec. 91.113 - Right-of-way rules: Except water operations.
(a) Inapplicability. This section does not apply to the operation of an aircraft on water.
(b) General. When weather conditions permit, regardless of whether an operation is conducted under instrument flight rules or visual flight rules, vigilance shall be maintained by each person operating an aircraft so as to see and avoid other aircraft. When a rule of this section gives another aircraft the right-of-way, the pilot shall give way to that aircraft and may not pass over, under, or ahead of it unless well clear.
(c) In distress. An aircraft in distress has the right-of-way over all other air traffic.
(d) Converging. When aircraft of the same category are converging at approximately the same altitude (except head-on, or nearly so), the aircraft to the other's right has the right-of-way. If the aircraft are of different categories --
(1) A balloon has the right-of-way over any other category of aircraft;
(2) A glider has the right-of-way over an airship, airplane, or rotorcraft; and
(3) An airship has the right-of-way over an airplane or rotorcraft.
However, an aircraft towing or refueling other aircraft has the right-of-way over all other engine-driven aircraft.
(e) Approaching head-on (in flight). When aircraft are approaching each other head-on, or nearly so, each pilot of each aircraft shall alter course to the right.
(f) Overtaking. Each aircraft that is being overtaken has the right-of-way and each pilot of an overtaking aircraft shall alter course to the right to pass well clear.
(g) Landing. Aircraft, while on final approach to land or while landing, have the right-of-way over other aircraft in flight or operating on the surface, except that they shall not take advantage of this rule to force an aircraft off the runway surface which has already landed and is attempting to make way for an aircraft on final approach. When two or more aircraft are approaching an airport for the purpose of landing, the aircraft at the lower altitude has the right-of-way, but it shall not take advantage of this rule to cut in front of another which is on final approach to land or to overtake that aircraft.
You use the word
"protected side" makes me think of (IFR) circling pattern "protected side". Visual pattern? There is no "protected side" of a visual pattern, just the pattern side. In fact I would suggest there are no guarantees or protection with any non-towered airport visual pattern.
I would hope my past students had the presence of mind to turn as need to avoid immediate objects with a soft or hard turn, left, right or just go straight ahead as needed.
My main goal in teaching balked landings was to smoothly add power, climb, carb heat off (cessna) and clean up. Than I expected them to navigate (turn if needed) and communicate. The usual drill or procedure was to enter the pattern again and land. I would have no problem with a pilot "breaking out" of the pattern to the non-pattern side if they felt it was prudent to do so. I would just ask why? There can be a good reason.
If you in your RV are overtaking a "spam-can" on the runway, its unlikely they will climb up into you. Just gas and go direct over them. You will have a hard time keeping visual contact as you overfly and pass them. The 500 foot separation FAR does not apply to taking off and landing. In fact some airports have taxi ways that cross infront of the threshold of a runway, overflying airplanes on short final with only 200 feet clearance, never liked it, but some airports like BFI have that configuration for the short GA runway.
Every situation calls for a decision to turn/offset or not. I just don't know of any hard an fast rule in the FAR's for a balked landing due to another aircraft on the runway. The Go Right RIGHT AWAY rule does not apply (in my opinion). If I have to take evasive action I'd turn any way I darn well pleased as PIC. I can deviate from any FAR. Runway heading is a good base line plan. For WAKE TURBULENCE AVOIDANCE you do step to the upwind side? The FAA and FAR's expect you to the safest course of action.
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Flying stories
I had a RV pulled on the runway in-front of me. I was in a RV as well. Despite my flying the pattern and calling all turns, he took runway position and parked while I was on short final? WHAT THE HECK? I later found out he had his kid with him. I guess he was distracted or briefing his spawn while parked on the runway with the radio volume down. I just added gas cleaned up level about 100 feet and started a shallow climb. I went slightly left (pattern side) only to not overfly the parked RV and it was away from the taxiway, hangers and folks on the ramp. Of course a week later this idiot chews me out for flying over him. Clueless to the fact I had the right of way and was on short final when he took the runway. There was no way I was going to do a 90 degree turn to avoid flying of his parked plane on the runway. Again the FAR about overflying people or things less than 500 agl does not apply on landing.
In another case at work, flying a B737, breaking out visual at 500 agl from an ILS instrument approach, tower let a MD80 take the runway. I flew straight with a slight turn to the left off the runway center line heading, just in case. Was told to contact departure by tower in a sheepishly way.
What ever you do don't get mad and just fly the plane. Stuff happens.