Newbee...
This initial set of conditions you stated could indicate an overcharged system, which is the apparent direction you took to remedy the situation. It could also have indicated non-condensibles as was mentioned, but let's look at this from the overcharge aspect as it's the more likely scenario of the two.
Since you said this an R22 walk-in cooler system, I'm assuming it has a TEV and a receiver. Does it also have a sightglass? If not, it should. A sightglass is one of your best diagnostic tools when dealing with the refrigerant charge on this kind of system because it can give you a benchmark of where your system charge stands.
Based on what you say you found on the initial call, I wouldn't have suspected a compressor valve problem. The high suction pressure may lead you to think that, but with that high discharge pressure I would believe the compressor to be pumping rather vigorously. An severely overcharged system would be the first thing to check.
To do this, rather than recovering refrigerant to arrive at some arbitrary set of pressures that "look good", you should watch your sightglass as you recover. The SG in an overcharged system will be clear...no bubbles or flashing going on, so as you recover watch for the first sign of flashing in the glass. Then add a little refrigerant until the flashing clears up. This is your benchmark, indicating where you then have a liquid seal in the receiver and a full column of liquid going out to the TEV. At this point, and when the box is at design temperature there is a minimum operating charge in the system. Add about 1 lb or so per HP beyond this point to allow for system load and ambient condition fluctuations. If the system has a Headmaster condenser flooding control, you'll have to add more to allow for cold weather operation. (That's another topic that's covered well all over this Forum.)
I suspect you simply went a bit too far in recovering refrigerant the first time and had to come back due to a low refrigerant charge condition. If you had initially used the sightglass as your guide and assuming all else in the system checked OK, that callback likely wouldn't have happened.
Now as for checking the compressor, as was mentioned, the valve you need to close off to check pumping efficiency is the suction service valve not the King Valve. When you pump down using the King Valve, you're pulling down all the refrigerant from that point all the way back to the compressor and that requires boiling off all the liquid in the liquid line and the filter-drier which can take a relatively long time. (I suspect the slow rise in suction pressure you observed was simply the residual cold liquid boiling off in the LL and FD.)
Although closing off the suction service valve is a common check for bad valves, it really will only tell you if your discharge valves are holding. You could have one bad suction valve and the compressor will still pump down into a good vacuum and hold it. The preferred method is to use the compressor manufacturer's performance data to determine if the compressor is doing what it's supposed to be doing at those conditions. Copeland's Compressor Performance Calculator is an excellent program to use for all of their compressors and is available for free download on their website. Tecumseh has tabular compressor performance data available online as well. If you don't have online access in the field, call your wholesaler and they should be able to do a quick check for you over the phone.
Also, when you check a compressor's performance and find that it's not up to where it should be, don't automatically assume that it's just bad valves. Of course, if it's a fully hermetic can, it's time for a new compressor, but if it a semihermetic before you run out for a new valve plate you should pop the head and do an inspection of not only the valves, but of the pistons. You could have a broken rod or piston. You should also check that the pistons come all the way up flush with the deck. Piston and rod wear can also cause serious loss of capacity and a call for a new pump.