The trick to the compression ring is to use a very fine screwdriver. Mine is closer to a jeweler's size; 2mm wide maybe. Then it is slipped under the ring and slid around and around repeatedly with each successive pass increasing the pressure to pry up the lip. Gentle & slow is best. Kinda like prying a tire off a wheel. It's a PITA for sure but only way. Too much pry-pressure & you'll risk breaking the edge but even if u do, it's usually not fatal.
A main reason for poor performance of the guage is not covered in the included pic/pages davido provided, even though this is a good how-to but the "stem" the author calls it, is not addressed; only the internal gearing. However, the stem contains the receiver for speedo cable & is a shaft that typically binds up with dirt in hardened grease. So even while you may have lubricated (and made pretty again) the guage it can still suffer from that input shaft being untouched. Example: speedo cable turns but input shaft is...reluctant due to contamination & hardened grease so cable "winds-up" until it overcomes the input shaft's restriction and then suddenly the dial surges. Voila, your speed goes boom and the dial's needle swings forward like you just dropped a gear & went WOT. Then as quickly back down when that input shaft's restriction acts like a brake. Repeat every second & you observe needle bounce...
This of course is possible from a poor or dirty speedo guage, cable or wheel gear.
What i do is put a "robertson" bit (the square bit) in a variable speed screw gun and test a restored speedo. You have to be CAREFUL not to over-drive the guage! It only has plastic gearing & limited speed input. IE: pull full grip on a typical battery powered screw gun & you'll see your speedo record about 1000 MPH for a split second before it melts down
Gently ease on the trigger & attain say 20 MPH and hold it for a few seconds as if you were riding the bike. No BLAM! 70mph. BLAM! Stop. You don't ride like that (unless you are ZukiDave at track day
)
This will help u see if your mech is healthy & functional before reassembly of guage tins, glass & bezel.
IMPORTANT: the screw gun has no problem over-coming a contaminated input shaft like the stock speedo cable may. So it won't prove the input is or is not dirty or reluctant.
If you test sanely & you hear squeeling, your guage is crying at you. You didn't get it completely cleaned. Most likely, that input shaft.
Now the bad news:
This input shaft is difficult to remove because it's under/part of, that magnetic disc. You will have to go deep into the guts below the odometer section.
Alternatively, you can use careful but liberal amounts of WD40 or similar and try to flush the shaft but success will be coin toss depending on possible seals in the stem. Also, even with success (lots of icky goo bleeds out of stem & input hand-spins easier), you still have not greased the shaft; just sorta hosed off the big dirt.
HTH.