Kamchatka,
Thanks for the complements! I will pass your good words on to those who helped create the aircraft.
Now, about your issue....
Initially, I will say that it does NOT have anything to do with the Pitot Heat. The pitot heat servers as the enabler for the takeoff trim under certain conditions, none of which permit it to server as the takeoff trim button while airborne. If not activated when needed, it will give a false indicated airspeed of 48 KTS. The Engine Anti-Ice serves as the enabler for the Automatic Throttle Control (ATC) function. The conditions for this function do allow for its use while airborne. I am not too sure how this effects the throttle performance at the altitudes that you have mentioned.
My best theory of what's causing your problems is the autoflaps function. As you mentioned, the slower you go while trying to maintain attitude, the higher your AoA will rise. This in turn causes the flaps to deploy further and further based on their logic. The more the flaps are deployed, the more drag is created by them, which in turn slows your aircraft even more, causing you to pull back on the stick to maintain attitude which exacerbates the problem even more.
The other problem is that most jet aircraft in FSX has flaws in engine coding, causing their efficiency to diminish as altitude increases, when in reality, engine efficiency is supposed to increase until around 36,000 ft. This forces many designers (including myself) to make a choice of either having an aircraft that performs well at altitude, but like a rocketship at sea level (i.e. default Hornet), or to have an aircraft that behaves nicely at lower altitudes, but under-powered at higher altitudes. Since our team's routine doesn't take us above 15,000 ft. I went with the later. The 2013 FSXBA variant that I am currently working on has corrected engine coding that allows it to increase in performance as altitude increase. So at sea level, the jet's maximum airspeed w/ AB is around 1.2 Mach and 1.8 Mach at 36000 ft.
For now, this can probably be remedied by making sure you have sufficient energy while climbing to those altitudes. Try to keep your AoA below 2 degrees or the flaps will start deploying.
As for the ILS issue, I will have to take a look at it when I get the chance. I am in the middle of a cross-country move right now, so I will check it out when I am back on my feet.
AI Carriers is a great product for those seeking to do carrier operations. I highly recommend using it in conjunction with VLSO

Thanks again.