You should not worry for your assets. Those are kept safely on wallet created from private keys kept on your ledger device. So as long as you have access to your ledger and its seed/pin/passphrase it should be all fine. In your case, restoring the wallet should make it work again. Open Monero GUI App and close any wallet which is opened by default. Choose an ...
It could be two things.
Your firewall is blocking the daemon from working. Try allowing a new firewall for monerod.exe
There is something that is using port 18080. If you know what program uses this port, close it before starting monerod.exe
There are two main possible bottlenecks: your internet and you disk speed.
Check how loaded your disk. If it's HDD and most time load nearby full, you can try to download blockchain on SSD (after that you can move it to HDD because you'll not download entire blockchain so it won't take as many time as first).
In other words, in there a command that lets me find the global index of a one-time output from its public key?
If you know (which it sounds like you do) the txid that created the output, you can just use /get_transactions, which reports the global output indices in the response field output_indices.
If you didn't know the txid, there isn't an RPC method ...