The following is what I ended up doing
Pretty much I cannibalized a pack of battery charging adapter plates, soldered the three wires to them, trimmed & bent them a little.. and then epoxied them down to the battery hold-down in their appropriate places. A little trimming was done on the plastic so the contacts could reach in far enough without obstruction.
After having the mouse sit around useless without a working battery in it.. for months, which definitely irritated me... I looked up 3.7V li-ion batteries and came across the "klic-5001 battery" (google it) and ordered two. The first one I destroyed trying to solder the wires directly to the battery contacts.. which just ruined all the internal li-ion battery components(i.e. DO NOT TRY DOING THAT)... the second battery, which I never tampered with whatsoever, is connected to the mouse via the contacts I described above. The klic-5001 batteries by the way do fit very well in the hold-down meant for the original battery.
End result: one, exceptionally well working MX1000 mouse which I can replace the rechargeable battery inside anytime it begins to get to aged and not working so well... ^_^ It charges as normal and the battery monitoring works like nothing ever changed.