Here's a trick I'll use, though since you don't have rogues it may not be directly applicable.
One thing that tends to slow down play is constantly stopping to search and look for traps. In addition to letting them take 20 on a search roll as long as they aren't in a hurry, I tell the rogues that while 'exploring', I'll let them use Search reflexively for traps.
That is, just tell me what door you want to go in. If there is a trap, I'll let you roll Search to see if you spot it before you open the door. However, if you fail that means you looked, didn't see it, and opened the door (or whatever).
As my players are as eager as I am to get things rolling, they like this idea.
One thing that tends to slow down play is constantly stopping to search and look for traps. In addition to letting them take 20 on a search roll as long as they aren't in a hurry, I tell the rogues that while 'exploring', I'll let them use Search reflexively for traps.
That is, just tell me what door you want to go in. If there is a trap, I'll let you roll Search to see if you spot it before you open the door. However, if you fail that means you looked, didn't see it, and opened the door (or whatever).
As my players are as eager as I am to get things rolling, they like this idea.