I agree with TT. The diluted poly isn't going to penetrate that far unless you made these chests out of 1/8" lumber, or, you soak the things in a bathtub full of poly.
Re-read the original answer about using BLO and making (or buying) some wiping varnish. If you make it and use naphtha, it will dry faster.
Bottom line and DAMHIKT, time is fleeting. You will need to let the BLO dry for a full 24 hours before using the poly if you want to really "pop" the grain. You can get 3 coats of wiping varnish on in a long day, but the more coats you put on, the deeper the finish will be, and look.
According to my calendar, you have about 3.25 days to get these done. If you hurry through it and try to take shortcuts or not allow something to dry...all your hard work will end up looking like, well, you know what.
If you wait any longer, I would definitely present them without finish, then take your time and do them right.
Just my 2 cents.