Iso-raising A3o is fine, then check twice and bluff river with A-high on a very connected board.
Flop T87cc is very draw-heavy and BU has the nut advantage; with A-high and no club, we should mostly check and let BU continue with their draws. Solver shows a strong preference for checking this combo on this texture, and a small c-bet frequency with some stronger holdings.
Turn 4h is a brick for our hand and doesn’t change the board’s overall connectivity, so we continue checking. BU’s range still contains a lot of club draws and straight draws, and our A-high without a club doesn’t want to face a raise, so checking again is the right idea.
River Jh puts a third club on board and completes a lot of straight draws; BU has more club combos than we do. Solver prefers checking A-high here and mixing in some overbets with strong hands, but a medium-sized bluff with A3o is acceptable if BU overfolds to river aggression. The 75% pot bet lands in a reasonable bluffing region.