One thing you could do to be certain that the problem is in the furnace itself and not the propane delivery system is to connect a regulated propane cylinder directly to the furnace itself. If the problem goes away then focus on the trailer propane system, if its still there then maybe the furnace gas valve or burner. 

I have not noticed this behaviior. Why don't you contact Airxcel and describe the issue? They might be better able to give you an answer.

I just had a thought. Have you checked the air inlet side to see if there are any obstructions (such as a wasp nest) in there? I have screens over all the vents in our RPod because I did have a problem with a mud-dauber nest in the refrigerator burner when we first bought our RPod.

I think you might be better off having a qualified technician check this out. Depending on the age of your RPod, it may be something covered under warranty. Even so, it is better to be safe than sorry. See page 2 of this document:

It it turns out that it is just a burner adjustment issue, that is not covered under the warranty. If you try to fix it yourself while any warranty is remaining, you will void your warranty.

Edit: I re-read the original post. While the 2 year warranty has expired, the additional 3 year heat exchanger warranty is still in effect.

If you do figure it out, don't forget to post the solution - I have used the search tool plenty of times to figure out what was wrong.

Everytime I fix something on our Pod, my wife and kids sarcastically ask me, "did you learn that from the RPod forum?"

I would check to see if your fan is either loose or the bearings are shot - sort of like the bathroom fan that is worn out.

that's the extent of my insight 

1. Fan comes on (no abnormal sounds).

2. Burner lights (tink sound followed by on and off abnormal rumbling),

3. Burner turns off (fan still on to blow out remaining heat - no abnormal sounds).

It is only when the burner is lit that the sound happens, and you can hear and fell the rumble going in and out during that time.

As far as my stove is concerned, I have not noticed the flame "jumping" but there is always a bit of variation in the flame height especially after you are just done purging the line.

Again, it's tough to troubleshoot based on words (kinda like when you tell you mechanic that the noise sounds like "shanana bop fweet":-)) so I hope my response is helpful!

I've noticed several things:

1. Before the burner lights (furnace fan running), there is no rumble. It only starts once the burner lights.

2. Sound is more noticeable in colder weather.

3. Sound is very noticeable from the outside furnace vent.

4. Hand over outside furnace vent makes the sound worse.

5. Sound is associated with a vibration that can be felt inside the Rpod.

6. Stove has a flame that jumps more than expected (not a very consistent flame).

I have had the propane pressure measured multiple times, and had the propane regulator replaced and recalibrated. The sound continues. I think someone else must have this problem?