Have you tried adding the additional directory nodes from github.com/JoinMarket-Org/joinmarket-clientserver/issues/144‌​5? I believe the default list doesn't have great uptime

Interestingly, 37paP4uTjmA4Pi85LG6CF9huift3Dw1kFT from the first spending tx is an atypical address. It requires no signature, and leaves a non-standard non-empty stack. In theory, those are "free" coins, provided you can get a miner to include the tx

If you're using a bog standard Bitcoin Core wallet, you fall into the Standard addresses, whether P2PKH, P2WPKH-P2SH, or P2WPKH category - to prove you control an address in the wallet, you would need to be able to sign a message with a key corresponding to that address in that wallet. Note that Bitcoin Core uses hardened derivations, so you would have to do this for each address that contains funds (as opposed to proving a single address and then sharing an xpub to show control of sister keys).