I don't understand how the transaction inputs can be stripped before signing.
input means the entire txin that consists of outpoint (tx hash and the index of the output being spent in that tx) the signature script and sequence. the inputs are not entirely stripped, only the signature script is emptied because there is no way to know the signature before signing the transaction.
a tx with 2 inputs and 2 outputs (to put simply):
[version]
[hash][index][sig_scr][seq][hash][index][sig_scr][seq][txout1][txout2][locktime]
to sign this for input 1 with SIGHASH_ALL you modify it like this:
SHA256d([version]
[hash][index][pub_scr][seq][hash][index][0][seq][txout1][txout2][locktime])
to sign for input 2:
SHA256d([version]
[hash][index][0][seq][hash][index][pub_scr][seq][txout1][txout2][locktime])
If only the Output is signed then a Miner could simply inject another UTXO from the same Bitcoin address and utilize the same Signature and give himself a big Tip (large transaction fee)
no they can't do that. as you are saying yourself
the outputs are signed that means the output can not change. even if the miner (or anybody else) added any other inputs they are just putting more money in that transaction that has a fixed output.
in fact this option also exists in bitcoin with another signature hash type called SIGHASH_ANYONECANPAY where you only sign 1 input that is yours and ignore everything else. it gives the option for others to add other inputs but you could sign all outputs and make sure no matter what others added the receiving end remains the same.
