This might be a tough one to diagnose. First off, a few questions.
If your outboard power trimmed while underway, both up and down, does it still do so? I don't work on the 225 but it is supposed to power trim while underway.
Have you ever hit anything with the outboard either while underway or while trailering? Impacts such as these can bend a tilt ram slightly and cause it to bind.
Have you ever trimmed the motor down when it was resting on the tilt lock? This can damage the pump.
Have you lubed the tilt shaft and the swivel shaft with a grease gun? Often an overlooked maintenance chore. Page 63 in the owner's manual.
Try manually tilting the motor up and down using the manual release valve and see if you can detect where the moaning sound is coming from. Page 58 (and others) in your owner's manual. Then, lock down the manual valve tightly and try the remote switch again to see if the problem goes away.
The link below has a parts blow up of the tilt mechanism. Look for any damage to items 9 and 22.
http://www.boats.net/parts/search/H... VIN# BAHJ-1300001/POWER TRIM-TILT/parts.html
If your motor is less than 5 years old, it may still be covered under warranty and you might want to take it to a Honda service center. There is always the possibility of water entering the tilt unit through the water seals on the tilt rams or through a failed O ring. This could be an early symptom of water intrusion into the unit.
If your motor is no longer under warranty, I strongly urge you to seal the wires where they enter the trim motor housing. USE ONLY OXYGEN SENSOR SAFE GASKET MAKER OR SEALANT!! DO NOT DO THIS IF YOUR MOTOR IS STILL UNDER WARRANTY!!!
Permatex Right Stuff is an excellent sealant for keeping water out of the motor housing but any oxygen sensor safe sealant will do. The bushing/water seal for the wires dries out over time and needs help.
Good luck.