Ways to shorten games between evenly-matched players

I play a lot with a friend. He's a little bit better than me and often wins, but as we've gotten closer in skill level, we're having an increasing number of games that are complete slogs - we're in a stalemate for hours, until one of us finally gets tired of it and either launches an irresponsible all-out attack or we decide to call it a draw.

The occasional slog can be fun, but constant slogs are not.

We typically play 1v1 on a Tiny map with Conquest victory conditions, and settings otherwise standard. We prefer to play the "standard" game - we're not really into Defend the Wonder/Capture the Relic where the gameplay is really different from normal.

Do you have any suggestions for how we can play shorter games that don't devolve into slogs?