As long as you don't have a line with an "else start next bid group" or "clear schedule and start next bid group", and just leave the generic "award pairings", it will do everything it can to give you a line, including ignoring any preferences you might have in. So if you are willing to sell out your soul to get a line and don't care what that line looks like, do that. You'll still want a RES bid group in under the REG group just in case it can't build you a line and forces you to RES.

Edit: the strategy in the post above works once you can hold a line - keep that carry over credit going to make it easier the following month to get a line. It does not work the first time coming off RES however since the next month's bids will be close and awarded long before you can get a RES trip assigned at the end of the bid period.