The common head found on a 55 motor is usually the 5913 head. That head is about 86 cc. Stock cr is advertised at 7.5:1 but they rarely get there, usually a little less. The 848 head entered service in 56 for the passenger cars. Trucks may have continued using the 5913 head later then 55, I am just not certain of that. I have a pretty early 848 head that has a late 55 (I want to say September or October) casting date so this head was for the 56 passenger car model year. 56-57 cr was advertised at 8.0:1. That changed in either 58 or 59 when the cr was advertised as 8.5:1. The chamber in a 59 to 62 head is 79.1 cc. I have never measured a 56-58 848 head to see what difference, if any, there is in the cc of the chamber. I will have to add that to my list of things to do this coming year. Just as a matter of completeness, the 261 heads come in two flavors, 86 cc and 92 or 93 cc (I forget which one off the top of my head).
As for boosting cr, other then custom made pistons (read that as very very expensive), you are stuck with milling the head, block or both. But it gets complicated depending on how much you are milling off because of the shaft mounted rockers. You have sink the intake valves a corresponding amount, raise the rockers the same, and add lash caps or use small block chevy exhaust valves with longer stems to the exhaust valves to keep the rocker geometry the same, or flycut the pistons if you are brave and think there is enough meat on cast pistons. Years ago they also furnace brazed the chamber to fill it up a bit to build compression. Milling the block is also a possibility. If you were to just mill the block, you would not necessarily have to deal with sinking the valves or lash caps, but you might, and you would have to have custom push rods (shorter by the amount you milled from the block) and adjusters made up (Smith Brothers can make them but only in 3/8 thickness). The Smith Brothers parts are a work of art (I have them in one of my 261 motors) but really over kill for a street motor. Then you would have to sort out whether the intake would hit the piston, depending on the lift and duration of the camshaft (necessitating a flycut on the pistons to make room for the intake valve or sinking he valve and all of that). No issues with the exhaust because of how deep the exhaust valve sits in the funky shaped chamber. I have done all of that and can confirm that its a lot of work and frankly, not a lot of return. there are other ways, but all of them require a good bit of machine work. If you want really good compression without lot of fuss, and it does wake these motors up, save and get a set of good pop up pistons from Ross. Not cheap by any means but the easiest way to get compression.
So unless you want to get deep into this motor, I would say leave the stock pistons alone, mill the head and block the minimum needed to get them flat and square.
Hardened valve seats, I have done them on occasion. Here is what I will say. I had a 848 head, perfectly good to start with, end up a boat anchor after machining for valve seats. Turns out the casting was a little thin in an unexpected place and the machining hit the water chamber. That was the last one I did and that has to be 20 or better years ago now. Truth be told, I have a 57 235 with a 55 5913 head with stock pistons in the back of my garage that I beat on unmercifully for years. It has an old Chet Herbert cam, 480 lift and 280 duration and stock rods. That motor never missed a beat and sounded terrific. When I pulled the head off to freshen it up, the valves needed nothing more then an old fashioned lapping. I did not use hardened seats on the 261 I recently built either (very modified) just for that reason so I would say skip the hardened seats unless you expect to drive the vehicle every day and put 80k on the odometer.
