I suspect there are 2 problems with the BX front tires. They leak at the rim seal, then because it's a low-profile tire you don't notice it's under-inflated thus you damage the sidewall. And then there is a soft spot on the tire. This soft spot keeps disturbing a SLIME seal, or it wears out the tube at that spot due to flexure. I wonder if, once you get them to seal, you should keep inflated at max pressure.
The BX gets TWO font tire problems, the 2nd cause by the first. I say slime them BEFORE they start to leak. Those are my BX tire theories.
Doesn't hurt to increase the weight of a BX - I had my tires foam-filled (more weight and flat-free) but it's a few hundred$. I sold my BX, after 160 hours, for more $1,000 more than I paid.
======== Here's my BX24 foam filling notes =========
Called TDS in Seattle, 762-3180 Anthony,
Quote estimate was $77 front, $112 rear, each, Turnaround in 2-4 days
Estimated 44 lbs in each front, billed for 51
Estimated 114 lbs each rear, billed for 133 lbs each
BX24 Front Tire Size 18X8.5-10
BX24 Rear Tire Size 26X12-12
They won't fill a leaking tire with foam because the foam could squirt out of the hole (during curing process), and you'd lose the "preset tire pressure". The foam "cures" in there and there's no possibility of a "do-over", no way to increase "foam pressure". You have to get the tire to hold air before the foam filling.
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This is with TDS (Tire Distribution Systems). I don't know about other foam-filling processes. I'm pretty sure they won't agree to fill it unless it's a very slow leak so you might slime it at the first hint of a slow leak, or just slime it now.