I lived in AZ for 20 years, and it is by far the most lenient state I know of in terms of DMV (or in AZ's case, just to be different, MVD) processes. Paying $100 for holding on to a title and not transferring it for a few years is kind of a pittance. There are other things you could try -- filing for an abandoned vehicle title which might technically be cheaper but would require a couple visits to the DMV, er MVD, and some time waiting. At this point, you might as well just wait. But if you've sure you've got a runner, who knows? One thing you can do to avoid late fees is ask to sign a "non-use waiver." In my early years in AZ I would go back to Seattle for the summer, but my bike's registration expired in July. I would come back mid-August and they told me I had to pay a late fee, but the first time they told me that the woman also told me about the non-use waiver. I signed it, didn't pay a fine, and did it every year after that I needed to. It might work for you even though it's a title transfer not a registration (the only thing that prevents you from doing so for registration is if you get a ticket so they know you were riding the bike).
The other thing I found is that penty of the folks at the AZ MVD appreciate a PMA. All day long people #$%* and moan about going there, but honestly if your time is flexible and you hit it at the right time, you can be in and out in 30 minutes to an hour. I bring a newspaper or a book to read. If you are friendly and conversational and just ask what can be done I think they have some leeway in assessing fines. I usually went to the MVD on McClintock in Tempe.
Another thing is to be aware of what you are trying to do. I went to register a little street legal TS50 and they told me I needed insurance, which isn't true in AZ for bikes under 50 ccs. even though I told them that I looked up the law and they told me they weren't sure, I had to go to another office where they just rubber stamped my registration. So it's not always effective, but best to be prepared.