"Tire Pressure Sensor Fault" appears in mssg center

[ExplorerRider]

Okay, I think I know the answer already, but this forum, & specifically an enthusiast namedh TechGuru, has really helped me, so here't goes... My TPMS system had been working fine, & I was curious about it whenever I went from P235 70 16s, the called-for tires, to a set of brand-spankin'-new P235 60 16s that I got for $5 apiece at an older fella's yard sale. But it continued to work. I thought I had all the broken glass swept off the back concrete pad, but I now have a very slow leak that a plug kit would most likely fix, and my TPMS system STILL alerts me when the tire is low, & goes out around 32, 33 lbs of air. So whenever I say that on my mssg center I thought, "Damn tires." However(!)... I turned the ignition on-off-on-off... til the horn blew, I jumped out & began deflating the driver's front tire, horn beeped, mssg center said "relearn right front." Began deflating, horn again successfully blew. It then said relearn right rear.... Started deflating. Horn NEVER blew, & tried two more times, always w/same outcome. So I have it narrowed down to the rear tires, & obviously, it's most likely the right rear tire. So my question is: Can I just buy a replacement, take the wheel off, deflate the tire, step on it so as to access the old & install the new TPMS valve stem, & do the manuel relearn myself? Or would it need to be an OEM valve stem to manually relearn them all. Walmart relearns them for free, but I only need one (2, tops) & they said they'd have to install an entirely new set of universal TPMS valve stems, & it costs $35-ish bucks per-tire to install them. Nevermind the fact that I'd also have to buy 4 new universal valve stems.... Trying to take an exceptionally clean 2005 Explorer XLT w/auto 4×4, that w/the exception of its not having the 289 V8 (aka 4.6 Litre) must've been ordered with ALL of the bells & whistles! Any & all thoughts or 'hard knowledge' greatly appreciated!