A joint Scottish Premier League and Scottish Football League plan to implement a 12-12-18 set-up crumbled last week when the top-flight teams failed to get the required 11-1 majority in favour.
While official talks on a new dawn for the game in Scotland stalled, the 10 Irn-Bru First Division sides as well as Second Division champions Queen of the South and Dundee - favourites to be relegated from the SPL - met on Tuesday night in an effort to breathe new life into the plans.
A working group has now been established to take forward a last-minute rescue package. An SPL2 that would exclude the bottom two SFL divisions has been speculated on as the favoured alternative and Strachan appeared to throw his own backing behind that when he said protecting full-time football must now be the "priority".
He said: "If you have got to make change, make it but make them big changes. Don't just tamper with it. Do it properly.
"For me, it's quite simple: if you are full-time, make a league for full-time clubs. That includes anyone who wants to be full-time, anyone who wants to bring in money and sponsors. They should be looked after first. That should be the priority of the full-time clubs.
"If you are full-time you are putting money, jobs and necks on the line. Part-time, you are not really doing that. You are a community club. So let's make a full-time league, and for the rest, go and have your own league. That would simplify it all."
The reconstruction plan would have seen the SPL and SFL merged into one body to offer a new structure involving a fairer share of cash and play-offs. But the bid was scuppered when Ross County chairman Roy MacGregor and his St Mirren opposite number Stewart Gilmour voted the motion down.
While Strachan - who was at Hampden to help launch PFA Scotland's search for Scotland's Manager of the Year - believes the part-timers should be excluded, the union's chief executive Fraser Wishart called for club chiefs to consult players and bosses.
"We've reached an impasse," he said. "But here's something radical, you could actually ask us and the players, Alex Smith and Craig Brown from the Managers and Coaches Association to come in with an input. At the end of the day, the people whose jobs are on the line are the players and managers."