Automatic bet. Think about your other hands as well. If you're 4betting a range, it will mostly be ultra-premium suited/connected high cards hands like AKKxds, AKBBds, KQJTds and such. Your range is so strong on this board that you should bet all of it.

Sometimes you hope he calls with hands you crush (like here), sometimes you hope he folds hands that have the pot-odds to peel (he's getting very good pot-odds against your good-but-not-great hands, like TP + gutshot). He will probably not fold too  much, but instead get it in bad a lot vs your range. Low limit players tend to do that.

When he's too weak to call, he probably won't bluff turns when you check flop, since that will look suspiocious with a range that should be betting this board 100%. If he won't bluff turns, you gain nothing by checking.

Your coach is 100% correct. This is an absolute MUST bet. You aren't likely to get him to bluff here (like actually, he is NEVER shoving a hand with too little equity to call your shove) and indeed he'll often take a free card with those hands which would have called off (random draws). Yes, you have this board crushed, but you gotta make sure any draw that's out there gives you the last $45 - imagine allowing this to check through and missing out on stacking a random heart draw!

This is all on top of the range considerations outlined so well above by Zen.

Just to chime in with the choir, it's absolutely a must bet spot.  The bet is so extremely profitable here, there's no way a check can be better.  Whether he folds, makes a bad call or calls with equity, it just doesn't matter since you profit in all those cases.  Checking is a sort of a holdem player mistake here.  The reasoning makes sense from a holdem perspective, but in PLO he's just going to have equity to call so often even if he knows you have the nuts.