Purchasing a circle track race car to run Lemons

As you have already said, the roll cage is the biggest concern, as it tends to be one of the most expensive and labor intensive parts on the car. And from what I have seen, nearly all of the cages built for circle track cars don't pass Lemons tech. The Honda you have posted for example, would need new down bars (curving the bar around the dash as seen in photo #11 is a no-no), new back stays (they should not extend beyond the rear wheel centerline nor should they cross), and is missing a diagonal support for the main hoop.
Also check out the fuel systems. Lemons requires either the stock tank and related components in their original location or a FIA rated fuel cell with a bladder and foam. A box with a fuel pump sticking out of it just won't cut it.
Another thing to look out for is compromised crumple zones. Lemons doesn't want to see severely hacked up cars or massive battering rams welded to them.

Other things to consider are stuff like tires that stick out past the fenders, under supported lexan or mesh screen windshields, welded up doors that make exiting in emergency situations difficult, and a few other smaller concerns.
While it is possible to get a circle track car prepped for Lemons duty, it's usually just easier to build one from scratch.

Most cages made for any other series won't pass Lemons tech (because most series don't enforce their own rules so well), so it's a good idea to send photos of the cage of any prospective car to Chief Tech Guy John Pagel before you buy.

I would second the buying a previous Lemons car.  There are tons of them out there, especially if you are willing to drive a bit.   

Another problem you will run into is Rule 4.1.1

The bold is where you will run into a problem.  Most people are fine when they buy an old Lemons car for $2k and then say that they spent $1500 on safety.  However it will be hard to justify spending $2k on a circle track car and saying its a $500 car because the cage was worth $XXX but I have to cut it out and replace it.

We have our hondas listed their.

I will make you a smoking deal on a package.

I hope you mean polycarbonate, such as Lexan, because plexiglass is acrylic and won't pass Rule 3.J.1.

Pros and cons....

I found my Lemons 1977 Pinto as an old retired non-running 1980 circle track Pinto a little better than a year ago.  The car was on C/L about 30 miles away, and was had for very little money.  It came with more spare parts and sheet metal than I think I will ever use.

The cage was a concern, but I knew that so much other work was already done that even if I had to swap it out I would come out ahead.  It had my favorite 2x3 box tubing down both rockers with the cage attached to them.  With new main hoop stays, and some other minor details, it should have passed tech. without issue, but I decided to go ahead and cut the roof off and remove it.  Before I started I sent some photos and details about the car to get approval, and it was granted.   I also sent some during the build process, including dealing with the fuel cell protection (see below).

The car also had full front and rear hoops to deal with, the front was easy as it was just remove it all, but the rear meant figuring out a way to keep the structure around the 12 gallon cell that was already in there and keep it isolated from the cage.  Photos taken and design approved. 

A DOM cage kit from Roll Cage Components was then ordered and installed, then the roof put back on.  The 2x3 box tube was also approved, it just needed proper spreader plates installed as if the box was not there.  EZ enough.  It was a great kit.  The only thing is that despite me telling them how tall to make the cage they sent it taller.  Not that it was a big deal, but I would have liked to talk about it more first.

I was able to sell the old cage to a circle track guy and get back most of what I paid for the car, but too bad it did not count.

Another thing was removing the suspension modifications that helped it turn only to the left. 

All said and done, for me, with THIS car, I think it was worth the hassle of dealing with the 'conversion' VS just building it from scratch.  There was enough here to work with, but it might not be the case every time.   You can score some 'go-fast' and spare parts, but as mentioned, every track and/or sanctioning body has their own rules that they might or might not enforce. 

Any car you look at needs to be gone over VERY WELL!!!  Bring at least one more pair of eyes, and a printed version of the Lemons rules, then look the car over as if you were the tech. at a race and this car's owner has just pissed you off.

Bill