Both the NFLPA and Spotrac have similar numbers for the Packers current team cap but for some I'm not capable of figuring out the players union website lists the team with an additional $3.4 million cap space.
Lets start with the NFLPA basic info (using round numbers) which has to be the definitive source assuming league contract approval followed by NFLPA posting has caught with the initial signing announcements:
https://www.nflpa.com/public-salary-cap-report
Previous Year Carryover: $3.9 mil (As an aside, who were those additional name free agents folks wanted signed last season? More than I care to recall. Champaign tastes on a beer budget.)
Team Cap: $173.6 mil
Cap Room: $10.9 mil
The first thing we notice is the stated Team Cap number is lower than even the league cap of $177.2 mil. Something's missing. It looks like it does not include dead cap.
$3.9 mil carryover + $177.2 mil league cap = $181.1 gross cap number - $173.6 Team Cap = $7.5 mil discrepancy.
both overthecap.com and spotrac.com show $8.0 in dead cap. That's darn close to that discrepancy. I think that closes one circle. The Packers gross cap number before dead cap subtraction is $181.1 mil.
That number is exactly what spotrac.com shows as the Adjusted Salary Cap:
http://www.spotrac.com/nfl/green-bay-packers/cap/
So far so good.
However, their $7.4 mil in current top 51 cap space is $3.5 mil light compared to the NFLPA. The Lewis and Bell cap numbers combined, as included in spotrac.com's current numbers, is $3.8 mil. Subtract from that number two guys they replace in the top 51 @ $550,000 each and you get a $2.7 mil deduction from the top 51 cap room for those two newest players. That's very close to the NFLPA numbers if the NFLPA has not yet posted the new contracts.
I agree with your earlier post that the 90 head count suggests these newest players are in that number, but who knows if there isn't also a lag in recording the cuts they replaced. Maybe they go back and re-verify the cap add for those cut contracts. Maybe somebody's on vacation. Or maybe spotrac.com is simply off by $3.8 mil on the individual contracts as you suggest. I'd wait a little while longer to see if the NFLPA numbers have more settling out to do.
overthecap.com has a different issue:
https://overthecap.com/salary-cap/green-bay-packers/
If you add their top 51 cap hit of $162.8 mil to their $13.7 mil cap space, you get an implied Team Cap of $176.5 mil, $2.9 mil more than the NFLPA data suggests. That would be a pretty obvious mistake that should be easily rectified which begs the question, "why haven't they?"
Anyway, subtract that $2.9 mil discrepancy from their $13.7 mil cap space, and you get to $10.8 mil in cap space, nearly spot on with the NFLPA number. One problem with that: they have not yet included the Lewis and Bell net $2.7 mil cap charge so they still appear to be off by that $2.7 mil.
My takeaway from all this is that for the aggregate team numbers, we're not going to have a better source than the NFLPA, allowing some time for announced contracts to be incorporated. For individual contract info, it's probably best to check both sportrac and overthecap to see if they are the same or close before drawing any conclusions. If one wants to get crazy with it, spot check rotoworld.com since they sometimes have nuggets of detail for individual contracts that the others don't include:
http://www.rotoworld.com/teams/contracts/nfl/gb/green-bay-packers?rw=1