I've had a quick playthrough with the mod and while I've not found any notable bugs, I do have some ideas for you to consider. I did the sound design for Mystical Mechanics (while doing work for Embers Rekindled) and while I was working on it I was considering my own ideas for a mod that used the Mech Power API. A lot of these ideas were actually very similar to yours, such as mech power generators for Botania and Thaumcraft, but since I know very little about programming I never got around to actually doing anything with them. Perhaps you'll have a better use for them:

• Power Generator for Blood Magic and Evilcraft. The Sanguinary Engine, as I would've called it, would add support for the two aforementioned blood-themed magic mods. The Engine would have two modes, one which would take in Evilcraft's Blood as a fluid, and the other which would drain LP from a Blood Magic Soul Network. In more detail...
• For Evilcraft, the Engine would consume Blood to generate power, probably fed in via an Evilcraft Entangled Chalice. In this mode, the engine could be upgraded with Evilcraft Promises (the mod's version of Machine Upgrades) for efficiency (Promise of Productivity), speed (Promise of Velocity), and tier upgrades to increase the max amount of promises the engine could hold (Promise of Tenacity I-III). These upgrades would only affect the operation of the engine with liquid Blood, not with LP.
• For Blood Magic, a small ritual would first have to be built with a few different ritual stones, with the ritual's layout being designed to allow for easy placement of axles and such, and then activated. The Sanguinary Engine could then be placed on the MRS, and while the ritual is active (and not disabled via a redstone signal), the Engine would drain LP from your Soul Network and create mech power. While the engine in this mode wouldn't accept Evilcraft Promises, the engine could be improved in a different way: Demonic Will. By attuning the ritual to different Will types and supplying the chunk with the apporpiate aerated Will, different bonuses could be achieved, such as increased speed, efficiency, or other more unique effects that I completely drew a blank on. Will upgrades wouldn't improve the engine in Evilcraft mode.
• Power generator for Astral Sorcery. Would drain Liquid Starlight to create mech power, either fed in via pipes or taken from a Containment Chalice. As for upgrades, I considered either upgrading it via Attuning it to specific constellations for different bonuses, or by pointing coloured starlight beams at it from coloured lenses.
• Power generator for Nature's Aura. Would drain Nature's Aura's... Aura from the surrounding area to create mech power. Would probably start off by default and activated with an RS signal so not to drain aura to avoid potentinally creating harmful effects immediately. I considered how an upgrade system might work, but I couldn't come up with anything.
• Essentia Generator thoughts. I had an idea for an Essentia Mech Power Generator of my own, which was essentially the same as yours except for the fact that it could take in different types of essentia for different stregnths/weaknesses. So Potentia essentia would be fast but drain quickly, Machina Essentia might last longer but be slower. Another idea I had for them would be that placing Infusion ritual booster runes under them would also affect them, both Efficiency and Speed Runes.
• Liquid Fuel Engine. Embers was originally meant to get an engine called the Underburner Engine, which would take in Ale (no, I'm not joking) or other liquid fuels like petrol to generate mech power. Essentially it would be an alternative to the Steam Engine. Not sure if this will be added to either Embers or its addon Soot, but it's something to consider at least.
• Another as-of-yet unused Embers idea was for a mech-powered spinning sawblade that could break crops once fully grown. It would also hurt players or mobs if they touched it while it was on. A bonus idea I had for it would be an ability for it to cut up logs into 6 planks, much like the saw from Better With Mods/Better Than Wolves.
• Catapult. Would take mech power to wind up, and once wound up would hold its power until released. When activated, it could launch the player, mobs, or other entities like dropped items a fair distance. Good for transport.
• Fan. Would take mech power and push mobs/entities/players away from them, or toward them if configured to do so via right-clicking or some such. Good for mob farms.
• Mechanically powered Crusher. Very similar to most other tech mods' Crushers, so it would double ores by turning them to dust (tripling ores if using Thaumcraft Native Clusters), crush cobble-to-gravel-to-sand, make dyes from flowers/bones more efficiently and would have various other recipes. Ore dusts would have been provided by Mystical World.
• Block Placer, Breaker and Interactor. If fed mechanical power, the placer would place blocks from an internal inventory in front of it (upgrades would allow it to place blocks in a wider range in front of it, perhaps even with modes for toggleable drawbridges), the breaker would break blocks (perhaps storing them in an internal inventory) and the interactor could perform different use functions, configured via a menu probably (left-click, right-click, sneak-click etc.).

That's a list of some of the ideas I had for a Mystical Mechanics addon. I do still have more, but I think that the ones listed here should probably be enough for now. Anyway, keep up the good work on the mod!

Those are some pretty good ideas, I'll definitely add some of them.

Glad to hear that my ideas may actually be useful. If you want to hear any more or if you need some sound effects, feel free to DM me on Discord. I am somewhat busy at the moment with Uni, but I'll try to help where I can. I'm in the Mystic Mods server, so go there for my Discord profile.

I'll suggest Immersive Engineering integration--make MM shafts take windmill/waterwheel power.

If you're still accepting suggestions, I would like to make few. If you're not accepting them, please let me know anyway.
PneumaticCraft: Repressurized: I suggest making mechanical compressor which allows creating air pressure up to some limit and pneumatic engine which will create mechanical power from pressured air.