Prima, $0.05/$0.10 Pot Limit Omaha Cash, 3 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $9.60 (96 bb)
Hero (BB): $10.52 (105.2 bb)
BTN: $12.14 (121.4 bb)

Preflop: Hero is BB with T 5 8 4
BTN raises to $0.35, SB calls $0.30, Hero calls $0.25

Flop: ($1.05) J 6 7 (3 players)
SB checks, Hero checks, BTN checks

Turn: ($1.05) A (3 players)
SB checks, Hero ?

What's the best option here? My first instinct was to bet because I have very decent equity and will very likely not win the pot if it checks through again. However, the A is a very good card for BTNs range so I'm not sure I wanna lead here. Getting raised would be really bad, too. If I x/c, I don't have the initiative OTR however and so will again very likely lose the pot unimproved whereas he'll either not put any more money in or have me dominated quite frequently on the cards that hit me. Does this make it a decent spot to x/r/f the turn and fire most rivers?

Since this seems like a result of playing a very marginal preflop hand: I wouldn't autocall this in the BB under any circumstances but don't think I can fold this 3handed, closing the action?!