. . . what's the best portable pump a man can purchase?
Well . . . first, perhaps we should DEFINE OUR TERMS!
As in, what does, "BEST," mean? Most reliable? Most durable? Greatest cfm (cubic feet per minute)? Highest psi (pounds per square inch)? Most compact? Lightest weight? Etc.?
Looking at, "reliable, durable," maybe . . . a MANUALLY-ACTUATED pump, such as one you might find at a trendy BICYCLE STORE. Or, outdoor store, like . . . REI, etc. Walk right in, sit right down, and ask the dedicated sales staff for what you want, and . . . chances are, the very product you need is available in stock.
Now, if you want an ELECTRIC COMPRESSOR . . . the big boys on the playground say, the "CADILLAC" of this category is a http://www.bestrestproducts.com
CYCLE PUMP (e.g., the "EXPEDITION"); lifetime warranty, made in the USA.
Leaning further toward KLRista frugalism, a SLIME pump, preferably a notch or two up from their small, very economical, "TOP-OFF" compressor, might do the job. Got one; stellar performance; bit of a weight and size penalty compared to alternatives, but compensating in performance, durability/reliability, all that stuff.
As to the $ 5 Harbor Freight-type overseas-manufacture mini-compressors (not unlike the one that grenaded on you); these often qualify as . . . JUNK, in terms of their material and workmanship, as illustrated in your example. One doesn't ALWAYS, "get what you pay for," but . . . sometimes, the axiom is fulfilled.
CO2? Hey; those systems really WORK WELL, but . . . how many CO2 cartridges must you CARRY? Example; you have a flat; you patch the tire; you inflate it with CO2, but . . . DUMMY, you pinched the tube on installation! Or, the patch doesn't hold! You think you fix it, expend your spare/reserve CO2 cartridges, and . . . it goes flat AGAIN! Where, in the middle of the forsaken Limberlost Swamp or the Dismal Swamp or the Gobi Desert are you going to find additional CO2 cartridges?
So, . . . you pays yer money and you takes yer cherce . . . good luck!
One question: Is airing UP a tire for gravel recommended? Just askin'!
As to, what to do about the run-flat tube you harbor . . . the prudent motorcyclist would demount the tire and inspect the tube. Most, however, would run it as is, keeping an eye on its pressure over forthcoming mileage. For SAFETY, I think the "book solution" would be to inspect the tube. Truth be told, I'm not sure what I would do in your position; might depend upon the service life spectrum I intend (i.e., just tooling around the 'hood, or launching a round-the-world excursion; a flawed consideration, perhaps, since a blowout even in one's neighborhood could have disastrous consequences. Inspect, replace tube as necessary, or . . . just plain replace anyway appears to be the safe path (tubes, after all, are relatively inexpensive; especially compared to human life and safety).