if we are balanced and not saying we should be, but if we were, we have something 3:5 or 4:5 ratio of bluffs to value depending on how turn sizing went. so when i originally saw this i thought that 55/66 might be folding pre to some extent. and our value hands would be 77/88/maybe 78s. so 6-8 value combos and we can balance that with AJcc, AQcc, A9cc, QJcc, 9Tcc.
Alright, i ran a pio sim. I think it's pretty obvious how to play this hand and pio largely agrees: I put all Axs in flatting range and all pocket pairs, 78s+. with less suited Ax and pp's because suited Ax 4bet sometimes and 55-22 play terribly out of position.
it will give a mixed strategy of: leading turn for 1/3, leading overbet, and check-call or check-raise. The leading small on turn range suprised me but it kinda makes sense now that i think about and see what it is. It's pretty difficult to put into your game with a overbet lead range as well though, so we could ignore it as it's a small part of the overal strategy and only does it 12% of the time.
It smashes overbet on turn with A6s, A5s, ATcc, A9cc, some Ajcc, AcJ, T9s, some 77, 44 and 88 and some AK ( i think its kinda weird to overbet AK). ignore the AA/KK combos there i have that weighted 10% of AA's/KKs, so that always be 4betting deep i think but i forgot to remove it from preflop ranges. So it's not exactly balanced on turn, only 30% of the turn overbet range is value, but that makes sense because the bluffing hands do have good equity, so it doesn't need to be balance because the semi bluffs have a lot of equity.
It will check-raise T9s, 87s, and check-jam turn with T9cc and a few 87 combos, and it will c/c turn with 88.
after it overbets turn, it will overbet river all A6s, A5s, AK, 88/77/44, some AJs/Ajo. it tends to prefer not overbet bluffing with club draws on river, and the overbet bluff hands on river are 90% A6s-A2s without clubs. But this is pio and it's way better at maths than humans, so i think its fine to just bluff river with your club Axs since not many humans would overbet turn with non club Axs, i think.
so yeah it thinks Axs are the best bluffing hands on river, because of removal and zero showdown value like you said. putting 66/55 in there is just way too imbalanced but if you think people overfold then go for it.