One thing to keep in mind is that over the past 25 years (720° was manufactured in 1984) the melamine covering on all the various 720° cabinets out there has been hit with varying amounts of sunlight.  The more sunlight a particular cab got hit with, the lighter the vinyl will have become.  In the case of my 720°, the sides of 'head' were darker than the sides of the 'boom box', and the sides of the main cabinet body were even a bit darker than the sides of the 'head'.  I matched to the area of the main cabinet body just underneath where the monitor overhangs, as that's the place that seemed to get the least amount of sun exposure in my case.  There was no side art on mine when I got it (it was very common for 720° side art to get peeled off while on location) but for those that do still have the original art, peeling a bit away would expose the virgin melamine underneath, which would be the best representation of the true color.

Having already rebuilt the rotary control, I brought the control panel and outer boom box panel to my local powder coater and when I got them back, I applied a new cpo and marquee overlay to them (both of which are high quality silkscreened art pieces from Phoenix Arcade).  These pictures of the overlays were taken post-installation:

The sides of the boom box were then stripped, covered, and new chrome t-molding was applied.  One important note about the boom box sides is that there are no screws keeping them in: they are glued and nailed.  You need to gently bang out the sides of the boom box with a hammer, and you want to do that evenly so that you don't bend the nails.  You'll want them in line when you go to put the sides back in.  I used a very small mm drill bit to slightly enlarge all the nail holes which made it easier to align the holes and push the sides back in.  I used the bottom part of my fist to gently bang them back in snugly.  You do NOT want to use a hammer as you'll ruin the vinyl.

Here's the order that you should use for the head/boom box sides:
 

1) Apply vinyl & chrome t-molding to both of the boom box sides 2) Apply vinyl & chrome t-molding to both sides of the head 3) Install both boom box sides (these must already be prepared  per #1 above)

You cannot apply t-molding to either the head or the boom box sides once the boom box sides are in place, so the above order is the only way to go about it.

Regarding the sizes of the vinyl you'll need to cut, for the sides of the main body be careful NOT to measure from the middle.  You want to measure from the front to the back of the utmost rear of the side (using 33" works perfect).  Lengthwise you can go with 43".  That little piece that sits low is 8.5" x 2", so it's best to pre-cut all that excess that you won't need beforehand.

The great thing about the cast vinyl that I used was that although it was thin, it was very strong, and I was able to use a razor blade at a slight angle (cutting away from the cabinet) which left me with a very slight excess (like 1/16").  That excess was folded over and then I applied t-molding on top of.   The vinyl clung very the edges very strongly and just looked perfect.

Here are some pictures of how the the cabinet looked after all the vinyl had been applied:

For the front, I recovered it with "Atari style cabinet vinyl" from Rich Lint at ThisOldGame. It really came out looking beautiful.

Other work involved installing a new switching power supply and the fan, along with replacing the inline Molex connectors for both of the boards.  It's a very common occurrence with 720° for these connectors to get blackened and melted over time/usage, so I highly recommend to simply replace them.

I also replaced the 4 blue leaf buttons.  Bob Roberts is the only place that I found that has an exact color match.  They are listed on his leaf buttons page as "BSPR Lavender Snap Short leaf buttons".

Additionally, I applied a "720° the ultimate aerial experience' decal that Jeff Rothe and Rich Lint graciously worked to get produced.  A huge thanks goes out to both of them for bringing this previously unavailable piece of art to market.  Also a big thanks to Wade Lanham for providing his NOS UAE sticker to Rich to scan and color match.  Here is what the original sticker looked like (you can really see how strongly the artwork yellowed over the years; this 'yellowing' is very typical of artwork that was used for titles that Atari Games made from the mid-late 80's):

Soy Gel (my stripper of choice, as it's non-toxic vs. brake cleaner, Goof Off, etc.) made short work of the glue and paint (not shown is that the sides were lightly sprayed with some Rustoleum satin black before application):

New UAE sticker applied:

And finally, due tot the efforts (and funding) of collector Chris Rhoades, I was able to replace the base t-molding that up until now, had never been available to purchase.  Every 720° I've ever seen has been in dire need of replacing its base t-molding.  For those that want to order some, leave a comment for Chris at the bottom of his profile page.

All in all, the restoration took a month to get done and cost roughly around $450.  A lot of that time was spent ordering and waiting for vinyl samples during the process of considering which vinyl to go with.

Once everything was done, the 720° was placed in a prime location in the arcade.