Well I'm not familiar with the 505 Gibbs version but have owned two CZ's, one in .416 Rigby with two cross bolts.

I can't help with recoil reducers.

Stock 'cross bolts' are usually part of the furniture (stock) and don't attach to the barreled action. As long as moisture doesn't penetrate past the bolt heads, they are fine to leave in-situ. A little stock oil like tru-oil or wax over the bolt heads before a major trip, is usually enough.

You should still be able to remove the barreled action from the stock for cleaning and oiling by undoing the forend and tang screws from under the stock.

CZ's are great rifles, some people find the stock wood not as hard as they prefer and there have been reports of stocks splitting on some forums from people who do not understand how bedding works. If you are used to a nice trigger, get the factory trigger rebuilt by someone who knows what they are doing. You will be amazed at the difference.