A possible way to hand wave not allowing AU to be field modified is by saying all mods over X size require specialized facilities.
I really don't think that there's any need to hand wave an explanation for why Augmented Engines might require specialized facilities to install. After all, you're making presumably significant modifications to your ship's engines, which should in theory be offline while you're doing this. Since you're also reducing the cargo space by installing Augmented Engines, it appears you're also rearranging the ship's interior and expanding the engine compartments, which suggests that you're cutting through interior bulkheads and rerouting power and cooling and fuel lines and installing the apparently sizable equipment that augments your engines. Since the ship speed (both tactical and burn) is increased, you're also probably looking at work on at least the thruster exhaust ports to prevent them from being damaged by the increased force exerted by the thruster exhaust.
If you think just a little bit about it, there's a considerable amount of work that would need to be performed in order to install or remove Augmented Engines, even if the ships of Starsector are all built with cargo holds arranged in such a manner that 25% of the available cargo space can easily be converted to engine compartments (i.e. all the required power, cooling, fuel, and exhaust lines are in place, there's reasonably convenient internal access for the crews, the compartments are airtight and connected to the ship's life support systems in a way suitable for more than temporary visits, there's adequate lighting, etc, and "all" that you need to do is clear the area and assemble the equipment). In my opinion, it's a lot easier to justify "Augmented Engines can only be installed/removed at a location with adequate shipyard facilities" than "Augmented Engines can be installed/removed whenever you want."
I'm particularly unfamiliar with the augmented engines perk myself, but from what I've been reading it seems to either take up some cargo space, or reduce it?
Perhaps a simple fix for the issue of fiddling about would be to simply apply the same effect to unstable injector, or simply remove it altogether?
The issue that Megas has with Augmented Engines is that they reduce cargo space on his ships in return for increased burn speed. Since Megas feels that he or she needs to pick up every last piece of loot from every last battle and must always have as much burn speed as possible, he or she finds it worthwhile to install Augmented Engines for the burn speed bonus, catch and kill fleets, and loot them until he or she has acquired enough junk to return to port. Since cargo overflow reduces burn speed and Augmented Engines reduce cargo capacity, Megas finds it worthwhile to go through and remove Augmented Engines hullmods from each of his or her vessels every time he or she acquires enough to cause a cargo overflow that reduces burn speed significantly, because removing augmented engines from every ship in the fleet increases fleet cargo capacity by 33% (assuming every ship in the fleet had Augmented Engines in the first place), which effectively boosts the fleet's speed because the cargo overflow is reduced or removed, and does so in a manner which is better than the burn speed bonus that Augmented Engines grant. This is an optimization that maximizes profits - dropping the Augmented Engines increases the fleet's speed and reduces cargo overflow, which results in a reduction in the amount of supplies consumed by the fleet en route to the closest station worth selling the junk to, which maximizes the profitability of the operation. Then, once all the junk has been sold, you can reinstall Augmented Engines to boost your burn speed again, and go around and do it again.
As a quick example, let's say you had a "fleet" of one Hammerhead destroyer. It has a basic cargo capacity of 100 and a base burn speed of 4. If you add Augmented Engines to this, the burn speed increases by 2, but the cargo capacity is reduced to 75. Let's say that you have a Hammerhead, install Augmented Engines to boost your burn speed to 6, fight a few battles, and pick up enough loot that you have X cargo where X is in the interval [150, 200) in your cargo holds. The current rule is that if you're carrying more than twice your fleet capacity of fuel, cargo, or crew, your burn speed is reduced to 1. Since 75*2 = 150 <= X, your Hammerhead with Augmented Engines is now reduced to a burn speed of 1. However, if you remove the Augmented Engines, your cargo capacity jumps back up to 100 units, and since 100*2 = 200 > X, your Hammerhead jumps back up to a burn speed of 4. Then, when you sell off all your junk and reduce the cargo carried back down to whatever your normal carried supplies are, you can reinstall the Augmented Engines and boost your Hammerhead back up to a burn speed of 6.