Are you absolutely sure they are 27" rims ?
If they are the smaller 700c - well, there's your problem. Maybe compare with an unlaced 700c rim and see if your rims are the same outside diameter, or bigger.
At a shop I worked at we got a pair of Sun CR-18 rims that were marked 700, but actually were 27". Thanks, Sun.
You shouldn't get blow-off at such low pressures unless you are trapping the tube between the tire and rim. There are lots of videos available about tire changing online. A few of them are actually helpful <G>. Try the Park Tool site if you are unsure.
If worse comes to worse just toss those #@$%&! rims and buy some actual hook-bead 700's and then you won't have to deal with all the tire compromises and trials and tribulations that you've been suffering. Be done with it . . .
Mike Fabian
San Francisco, CA