"However, the US Exp Category doesn't have the silly weight limits which the European light/sports stuff has to fit under so they can be reasonably robust, and a suitably built/equipped plane can then be flown IFR."
And of course, Permit types aren't forced to be under the LSA weight limits either - there really is no valid reason why a Permit type, per se, could not be perfectly fine for IMC/Night. Of course there will be issues of who authorizes the equipment fit if the aircraft is not certificated - LAA Inspectors might not necessarily be qualified to do that, but I wouldn't have thought the problem is insurmountable.
As for the single engine at Night issue, that should be up to the pilot to decide. Permit types are no more likely than Certified types, with similar or identical engines, to suffer engine failure.