Yep-- now these aren't pretty, but:
I figured a tapped LC circuit would need somewhere around 6.5 uH and 20 pF, and since RG-8 has 30 pF/foot a 10" length or so would work for the capacitor. An online calculator showed an air-wound coil with 10 turns in 4" with a 2.5 in diameter would be about 10 uH, so I figured I should be able to find a tap on that someplace to match 50 ohms at 14.175.
So I bought 10 feet of #8 bare copper at Home Depot, and started looking around the garage for something close to 2.5 inches... All the pint paint cans and spray paint cans have that lip on them, so I ended up using a white vinegar bottle, the plan being to hold the turns in place with epoxy. That turned out to be not such an easy thing, so this is what I came up with for that:

The 1 minute epoxy ran more than I thought so it's not very neat-looking, but it worked:

The coax capacitor was just soldered across the coil:

Test setup with the noise bridge and VSWR meter, using a 4.7K resistor across the coil. 3rd turn on the coil and about 2 1/2" trimmed off the coax made for a near perfect match (whether it would really match the end of a 1/2 wave remained to be seen):

I picked up a 6x6 inch weatherproof junction box while at Home Depot to mount the matching network in:

Long story short, I didn't have to change a thing when I got it connected to the actual antenna. I cut the antenna 1" short to compensate for the lead between the coil and the antenna (and as a SWAG for the velocity factor of the insulated wire), and that helped a bit as the antenna favors the low end of the band but is still under 1.5:1 at 14.350.
This is the feedpoint with eveything mounted- that coil of coax is the CATV feed:

So there's the whole thing:

I figured if it didn't work I'd remove the matching network and use a 1/4 wave section of open wire, maybe even make it a J-pole since it was 16 feet to the ground. The mast is just spliced-together 16' sections of 2x2 that were made from ripping a 16' 2x4.
The key word here was cheap, and I nearly pulled the trigger on ordering a 4BTV, but decided to try this first since I'd only be out a few bucks if I didn't like it.
Hope that wasn't overkill.
Rick