111 watts x 4 is a pretty big amp. Is that the RMS rating or max?
I would go ahead and attempt to run new wiring. You wont need anything bigger than 14-16 gauge. But I am not too familiar with the 2002 Accord's door. If they are similar or the same as the new 07s then i can take a look at my friend's car to see if there is an easy route.
You say that the stock location gives poor imaging. Imaging is mostly due to the location of the speaker and where it is pointing...will replacing the tweeter but keeping the same location fix that problem? You always have the option of hacking a hole into your door panel or sail panel to house a new tweeter...but that will pretty much be a permanant mod.
A better option would be to leave the tweeter as is, and replace the woofer with a coax setup. There are higher end coax setups that allows the tweeter to pivot. I've heard a CDT coax used as a front stage, and it sounded awesome. The car was an Integra, and the speaker was placed on the lower left of the door. The tweeters were aimed at the opposite side headrest. I believe the speakers were
these. This option will still require you to run new wiring though. I am not sure what is required for your transceiver, but if all you need is a tweeter, then you always have the factory one dedicated for it.