For the NFL, treat it just like a regular 15:00 period. Have a kickoff - everything. But, but BOTH teams have an opportunity for possession. I.e., Deadskins kickoff to Cowheads. Play continues by rule, except both teams must get the opportunity to score a TD. If the Cowheads score a TD, then they kickoff to the Deadskins, so the Deadskins have the opportunity to score a TD. If, after both teams have had the opportunity to score TD, and they are still tied, play continues as any other period, until one team takes the lead (after a try, if a TD is scored).
Example:
Deadskins kick off. Cowheads return kick to the B-40. Cowheads have scrimmage series at the B-40. Cowheads score a TD, plus a Try field goal. Cowheads up by 7. Cowheads kick off to the Deadskins (touchback). Deadskins get a scrimmage series at their 20. Deadskins score a TD, plus a Try field goal, to tie. Play continues as normal. But, the next team to score wins.
Example:
Deadskins kick off. Cowheads return kickoff for a TD, plus score a Try field goal. Cowheads kick off to Deadskins - touchback. Deadskins have a series from their 20. They fail to score after a 4th down. Game over, Cowheads win.
Example:
Deadskins kick off. Cowheads return kick to the B-30. Cowheads have scrimmage series at the B-30. Cowheads fail to score, and punt on 4th down. Deadskins begin a series at the B-15. Deadskins kick a field goal. Game over, Deadskins win.
Just like hockey, play continues for up to 15:00. Then a 10 minute break, and do it all over, if necessary.
What's wrong with that?