Which block header fields are miners able to change in an effort to avoid having to recalculate the Merkle Root? In addition to the nonce and the Merkle Root, there are 4 other fields in the header - version, previous header hash, time and nbits.

Assuming a miner does not want to change the merkle root because of the additional computation involved, and obviously cannot change the previous header hash, to what extent are they able to change the version, time and/or nbits field to get additional nonce space?
nBits cannot be changed at all. Its value must equal the (compact encoding of) the target value for that block, which is determined entirely by the predecessors of the block. In other words, if the prevblock hash is given, so is nBits.

nVersion: can be modified arbitrarily, though its value is subject to interpretation under BIP34 (requiring it to be at least 2), BIP66 (requiring it to be at least 3), BIP65 (requiring it to be at least 4), and BIP9 (assigning potential future meanings to certain bits if the value is within a specific range).

nTime: can be rolled within a window starting at the median of the past 11 blocks + 1 up to 7200 seconds in the future at the time the block is mined.