Soldering the brass pad - clean it good on one side, appiy a little solder flux,touch hot iron to it(still not in module, on a heat resistant surface) then touch solder to it - some solder will flow across it almost immediatly. Clean module contact, small wipe of flux(very little is needed, just the thnnest film), lay brass contact with soldered side DOWN, touch hot iron to top(battery contact) side for just 2 seconds. Pull off iron and blow on contact to cool. You are done.
Before you go on to the quartz: since your module was doused in the acid, a Hughes module will often, due to the ceramic substrate, have a lot of metal salts stuck to their surface, leading to erratic issues, such as stuck on, jumping thru settings,etc. Take a Q-tip and some clean water and wipe the board down good on the battery side and on the front side all around the LED cover. Or use a mild alkaline like the stuff for removing hard water spots from bathroom fixtures(I use CLR brand, personally). I've "fixed" many a Hughes module that was erratic by merely cleaning off the battery juices that dissolved some of the contact metals and then left them as a fine trace across or around the circuit board. There's not much you can hurt on a Hughes board. Bulletproof!
The quartz crystal. You don't have to remove the cover. Mix up some silver epoxy, dip a needle or other pointed object into it and pull away so you have a pointed "Drip". Gently stab that into the first hole(three on most Hughes, some later had only two), repeat for each hole, get a nice dab into them. Take a Q-tip dipped in some alcohol and clean off all smears outside the holes very good, then press the crystal back into the holes. Don't be tempted to put some on the crystal leads or leave some mounded outside the holes, whatever you get in the holes will be quite sufficient.[If it doesn't work, pull the cover and see how much got thrugh to the other side - although, there may still be a "cap" of the original silver epoxy over the holes on that side.] Then mix up some regular 5 minute epoxy and just put a small dab at each end of the crystal to hold it to the circuit board - the silver stuff is not very strong, mechanically speaking. Hold the crystal until the regular epoxy is set or put a rubber band or very weak clamp on it...I find those plastic clips meant for half-empty potato chip bags are a good, weak clamp. Wait at least 12 hours before testing the job - the silver epoxy conducts electricity much better when fully cured. Don't know why, just seems that way.
Those plastic "chip clips" - I find a big, wide one, with soft rubber on the jaws, is just right for holding a glued on Pulsar or Frontier module display after silver epoxying.
Mmmm, chips, beer, epoxy.
Sorry I got so long.