Yeah - that string / intonation will follow you around like a stray cat, and your post most certainly illustrates their overall importance in the grand scheme of things. If you can afford the bone$, I'd do the mods all at once. Or, leave it stock until you've acquired all of the parts you're planning to change out. That way, you're not having to re-adjust everything all over again after replacing each individual part.
Those Fender Script Schallers are straight-up change-outs on the Squier Tele Std. - no scars at all, and look factory spec (and WAY better than the stock units). However, I'm not sure about them working on the '51. I'd check out the specs on the Fender / Squier website just to be sure. The neck on the '51 looks almost identical to the the ones on the Affinity models & Squier Std.'s, so I think there's a good chance they'd work. I have a number of good web and Ebay links for aftermarket parts that would work with your Squier, too, so if you're interested, let me know.
I think all totalled together (p'ups, tuners, pickguard), those parts were right in the $150 range, not incl. installation or set-up following. But they turned that guitar from a decent home practice player into a rock-solid rig that would hang with anything you threw at it - gigging, recording, jamming, etc. These guitars are a STEAL at $200 US. Spec out a few choice upgrades, and now you're walkin' the real Fender walk!