IME, Slime sealer and thorn resistant tubes will slow goathead leaks down enough to get by with...at least at MTB/cruiser tire pressure. You will still need to pump up your tires every few days though.

The Mundo has plenty of space to carry a floor pump if you can't afford a frame pump at this time. Actually, most of the frame pumps on the market are pretty sad affairs, IMO. I once had a Mt. Zefal that worked really well. Some thief got it.

Actually, I run 60F/80R psi on my commuter, and regular tubes with slime, and it seals the pinholes that goatheads leave OK, IF I can resist pulling them out when I stop. About once every couple weeks, though, something will make about a 1/8" slit in the tire. I think it is glass shards maybe...never stays in the tire. The slime will seal that in about 20', then let go again about 50' later. Basically it only allows me to choose a nicer spot to stop and fix it. When I fix those, I usually find 1-3 goathead pinholes as well. My commuter is an IGH, so painful to pull the rear wheel on that, and yes, it seems that about 90% of the time it is the rear wheel that flats rather than the front.

If you use slime, carry some alcohol wipes to clean it off the tube, or the patches won't stick right. Also, the "no glue" patches are temporary at best. All the time is spent taking the tube out and replacing it anyway, so it only takes about 5 more minutes to do a proper job ONCE, with glue and a Rema patch...but I carry a couple of the sticker patches just in case my tube of glue is dried up when I need it.

I carry some ropes for securing the load, and have used that a couple of times to suspend the frame from a street sign pole as an improvised work stand. Standing the bike on the seat and bars tears up your seat, hand-grips, and bar candy.

It IS possible to patch a tube with the wheel still on the bike: Not real easy though, and I find that I am not patient enough to make a good job of it but about 75% of the time. The hardest part is trying to find the object in the tire that caused the leak. Standing the Mundo on it's butt might make that easier.

Another thing you can do is leave a spare tube inside the rear triangle, tied up to the left stays (rack on the Mundo) so it doesn't drag on the wheel, brakes, etc. Looks like heck though, and you still have to find the thorn or whatever in the tire.

As I said, I am going to try the Cobra tubes and see how that works. I saw a mechanic putting one in a share-bike when I was in Paris, and it was a forehead slapping moment. Took a lot of googling to track them down, as I didn't know what they were called. Too bad they don't come in 700C sizes, but maybe they don't work so well with skinny tires. They are $11 at Universal bikes.

If you are trying to save some money, check the bike isle at Target. They seem to be have stuff on clearance frequently. Last weekend I picked up a seat wedge bag for cheap, (I forget the price) and a LED headlight for $5. Not a great light to see by, but a pretty good "be seen" item. They also had patch kits for $1.48. It had the "no glue" patches I don't like, but came with a serviceable set of tire levers.