Have you ever gotten in a total lock-up like this? Is this a draw?

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[Link "https://www.chess.com/play/computer?moveList=d5e5+g4g3+h2g3+f4g3+e5f4+b6b5+f4g3+b5c5+g3f3+c5d5+f3g3+d5c5+g3f2+c5d5+g2g4+d5e5+f2g3+e5f6+g3g2+f6g5+g2g3+g5f6+g4g5&fen=8%2F8%2F1k5p%2F1P1K4%2F5pp1%2F8%2F6PP%2F8+w+-+-+0+54"]

1. e4 {Time to let the queen come out.} 1... e6 {Qg4 coming soon $2} 2. Nf3 d5
{I'm coming at you $1} 3. e5 Qd7 {Don't you just love queens $2} 4. d4 b5 5. a3 c5
6. c3 c4 7. b4 Na6 8. Nfd2 Rb8 9. f4 Be7 10. g3 Bb7 11. h4 Bc6 12. Qg4 {What do
you think you're doing $2} 12... g6 13. Qf3 Nxb4 {There goes a piece.} 14. axb4 h5
15. g4 f5 16. g5 a5 17. Ba3 a4 *

I kind of did this intentionally and Black played along but still it is so odd.  

Yes. I can't imagine any way of avoiding a draw.

White had a chance until the very last move to have at least one open file.

Good point. That's what I ended up doing.

Depends if the backwards pawns can be targeted at all by either side - defo tricky to make progress but one side will likely struggle more to defend every “support” pawn in the chain

In that way, I’d say the side with more knights has the edge because of the closed position

tbh, one side must sacrifice something, or this must be a draw.

A good example of this is a game by Capablanca which he ended up winning against a decent player (I think it was Emanuel Lasker but idk) so I think it is possible to win... but you have to sac eventually yeah.

I haven't gotten that before