Again you're almost there. You lost this one by a whisker.
Lost Glider is a garrison heavy map. The mortars were a good call for deterring building camping but I'd also have prioritised the pioneer's flamethrower over LMGs for your Grens. It's a very effective way to clear buildings. Use flanking or mortar smoke + attack ground to get in close enough if you're fighting an HMG.
You were behind on fuel because you didn't cap your cutoff at the start of the game: you weren't getting any resources from the points you took.
With Ostheer your army works best when it works together. By separating your team weapons your opponent is able to exploit their weaknesses. Your HMG gets forced back by flanks and vehicle attacks, infantry walk up to your mortars, kill the crews and steal them and your AT guns get flanked.
If you cover your mortars and AT guns with an HMG they're protected from infantry attacks. If you protect your HMG with an infantry squad it's harder to flank. Infantry can scout ahead for your tanks so they don't drive into an AT wall like your poor Tiger did and believe it or not they're critical to killing vehicles.
If you have an infantry squad with a snare (an ability that cripples mobility) near your AT units they become much more effective at killing vehicles than they would be alone. Once a vehicle is damaged hit it with a panzerfaust. That damages its engine so it can't get away, allowing your tanks and AT guns to kill it fairly easily. Even if it retreats into smoke you can still hit it with Attack Ground. Keeping a Grenadier squad near your AT guns and tanks allows them to quickly snare any vehicle that tries to attack.
Finally a few small details.
- If there's a dropped LMG try to pick it up with a Grenadier squad instead of a Panzergrenadier squad. Panzergrenadiers fight at short to mid range, Grenadiers fight at mid to long and LMGs work best at mid to long.
- Suppression spreads between units clumped together. If you've got a squad in green cover (and therefore with suppression resistance) fighting an HMG don't move another squad into that cover. They'll get suppressed trying it and that suppression will spread to your otherwise immune squad.