It's different thicknesses of cap metal for pry offs vs. twistoffs. So your pry top cap isn't going to crimp as nice on a twist off without the right cap.

This is based on too many years experience..

There are two quality parameters one should measure to assure the quality application of a crown.

1. CRIMP: The incoming crown is flat and wide. After application, the crown's diameter is smaller. It has been "crimped" on the bottle. One measures the diameter of the crimped crown while its on the bottle to make sure the resulting size is within specifications and the crown has been properly applied. As you know, there is a spec for everything.

When I was doing my QC thing we were using industry standard 12 oz. NR bottles. The limits were 1.125" to 1.140". We normally ran 1.130" to 1.140".
A 1.145" crimp was runnable but needed to be corrected at the "earliest opportunity." A tight (low number) crimp runs the risk of bottle breakage ; a high crimp (high number) hurts the hands when opening and could possibly leak.

Crimps are measured with a simple gage. Its a stainless steel bar, maybe 6 to 8 inches long and the bar has holes in it. Our crimp gage had holes of 1.120-1.125-1.130-1.135-1.140-1.145-1.150. To measure crimp one lays the bar over the crowned bottle and finds the hole that the cap can go through. If the bottle top won't go through a 1.125" hole but will go through a 1.130" hole your crimp is 1.130".

2. TORQUE: This is a measure of the ease (or unease) of crown removal. Torque is measured in inch pounds. If torque is too low, you risk having leakers along the distribution chain. If the torque is too high, the cap is difficult or impossible to get off and you piss off your customers.
Again, there is a spec for everything. Torque specs will vary by package.
Our specs for the standard NR were a minimum of 6 and the max was about 11.
We measured torques with a "torque gage" Its a meter that holds the bottle while the operator twists off the crown. The answer is read on a screen on the meter. You can also rig up a torque wrench to a fitting that fits over crown . That's all you really need.

If your torques feel loose, they are loose. But you need to be measuring them.

CORRECTIVE ACTIONS:
CRIMPS are easy. The problem is usually worn throats/wrong throats or a head that needs raising or lowering.

TORQUES are harder to control. From experience I can tell you there is very little you can do to fix/control torques in the brewery. Its usually a crown or glass problem or a compatability issue between the two. A large brewery can get materials changed but a small brewery has little clout. I'm guessing you are a little guy.

Torque is largely determined by the lubricity of the compound in the crown. Big breweries work with crown manufacturers to dial in crown compound lubricity and resulting torques. Twist off crowns have more lubricant so they can be easily removed. Pry off crowns have less lubricant. If you put a pry off crown on a twist off bottle, you can twist it off but it will be harder to remove.

RECOMMENDATIONS:
1. First you MUST measure your crimps and make sure they are in spec. Have a crimp bar made. Even a go/no go gage will work but a bar tells you much more.
2. You MUST get a device to reliably check torques. You need to know what you have so you can tell if the corrective actions work.
3. Get with your crown supplier and enlist their help in addressing the low torque problem. They may have crowns for testing purposes that vary in lubricity. Run some tests and see what happens.
Let's assume you are running the correct TWIST OFF CROWNS. GET SOME PRY OFF CROWNS and run a test. They should have less lubricity so your torques should get higher. Maybe that will be the answer.
From experience, crowners can very significantly in the torques they produce. Some crowners give torques that are chronically on the low end while others yield healthy torques. It appears your crowner is one that gives
QC people gray hair or no hair.

And one final thought. There's not much of a relationship between crimps and torques. You can have bad crimps with good torques and you can have good crimps with bad torques.

Please keep us informed of your progress. And if there are any folks out there who have better ideas or think I'm smoking something, please chime in.