Having users pre-sign transactions for later submission usually isn't viable. Instead, consider having them sign personal messages as a proof of vote. These messages could be stored and submitted later. While you can't directly batch votes into PTBs, administrative contract features might allow for efficient vote-recording methods on a backend, potentially reducing the number of necessary on-chain transactions.

PTBs might not help, as you can't combine transactions from multiple users in a PTB. However, if your smart contract allows it, you could create a transaction that records votes for many users through an admin cap and submit this through a cron job. This might condense and reduce transactions as compared to processing each vote individually.

Sponsored transactions could work for your situation, but you'll need a backend to handle transactions. Enoki might be a good starting point if you go for the sponsorship route. However, consider using a backend that submits transactions where users sign a personal message for address validation. You still need the backend for transactions, but it might lower fees than individual processing.