You should be able to spend several weeks painstakingly restoring water-pressure to a school just to flush timed-explosives down the toilets for a large morale buff.
Most professions should have a building associated with them. If a character destroys a building associated with their profession, then they should get a morale buff.
If a ‘mindless’ opponent is slower than you, then you should be able to automatically stay out of its reach(this would take time, and could be interrupted by things other than the target) while sticking a sticky bomb to it with a stick. You can then walk away from it and remote-detonate the bomb for a morale boost.
If you pile more than a megaton of explosives in a single location, then detonate it, it should provide a morale buff.
You should be able to combine several layers of advanced armour with a crude bomb-launcher to build a rudimentary orion-drive for vehicles.
You should be able to throw high-explosives into waterways for morale buffs and foraging.
You should be able to build orion-drive roller-skates.
You should be able to build reactive armour. You should be able to mount that reactive armour to conventional armour, you should be able to mount a plate of such a combination onto a heavy, rigid gauntlet. You should then have a specialised punch option.
You should be able to put anything you want into microwave-ovens and then put them on a timer…
You should be able to attach remote-detonated bombs on dogs.
You should be able to put magnetic-triggered anti-vehicle mines on dogs.
You should be able to put dogs into sealed reinforced-glass chambers and then expose them to various doses of glob or mutagen and observe the results.
Or maybe we just need a dog-deterrent that makes them want to leave the character alone.
You should be able to disable the arming sequence on a thermonuclear I.C.B.M. and launch it to a specific location for salvage.
You should be able to attach a thermonuclear warhead to a metal plate and a rigid gauntlet and put it on a hulk zlave’s favourite fist and then send it at a tankbot.
You should be able to use explosives and some basic chemistry to build fireworks that can provide a morale boost but tend to attract hordes, but the morale boost should have a massive range and the fireworks should be remote-activated.