I am solo mining with my own blockchain and wallet hosted by me, I have opened the firewall to allow inbound connections, not just outbound, I figured it may be relevant in the off chance of success.
To answer your original question, getting on a relay network will help. You want to be mining on the latest block as soon as possible and you want the major miners to start mining your block immediately. Read this:
https://galaxsis.com/posts/bitcoin_relays_part_1/