I pretty much do things the Tapanojum way. Reduce the size of your military and take more risks, leaving behind small garrisons and advancing with half-stacks against full-stack enemy armies. You should never really let yourself dip more than a few thousand mnai into debt, for the reasons you've just shared with us.

If that sounds a bit tricky, you've got another option. Disband practically everyone right at the start, and focus on building up the economy of your core provinces until it can support the expeditionary force you've always dreamed about but have been afraid to mention at parties.