Mission 3 and 7 can be cheesed with HQ caps via just sneaking towards their base with an infantry unit in an APC. Admittedly this is a bit tricky with Mission 3 since you have to bait the recon into attacking your initial APC from below, but you can increase the odds by dropping your infantry momentarily on the Northern most city on that map.
If the recon takes the bait you can then reload your infantry into the APC and make your way into the woods to a position that can't be reached by the nearby mech nor the recon because it's to far away. Though if creating another APC at your southern starting factory influences where the AI attacks is unknown to me. I didn't test the map enough to work out if the recon's position is manipulated by this or not.
At any rate after getting into the woods it's a straight shot through the woods and down the road to the HQ since capturing units won't stop their caps to take out the weakened APC and due to how units are spawned on that map you should be able to place your damaged APC on the enemy's factory near their HQ. The one infantry unit close enough to respond will then spend it's time attacking your APC as you cap the HQ. And any other units that could try to get their in time just ignore the issue and move towards Sami's base.
Unfortunately while I'm currently doing videos for this game again. Those videos are going to be coming out in June so unless you want me to send you the file you'll have to wait a while to see the proof.
Though you can HQ sneak faster on Mission 7. In fact, you can finish it in 7 Days using the APC rush strategy. This is mainly because the enemy seems to really hate APCs for some reason. I assume it's a nod to "Advance Wars" on the GBA.