More of a medium duty issue...

Allison AT545 are a light duty transmission, they were a great school bus transmission.
The shift points are adjustable. There should be a cable for a throttle valve on the left side of the trans, running to either the foot pedal or injection pump linkage.
That adjustment varies the shift point based on throttle input.
All of mine were adjusted correctly and would shift at up to 2500rpm.
They are a bit of a turd for pulling, no lockup converter and very little engine braking, and only in 4th

 

I once owned an older International with mechanical dt466, air brakes, and 10 speed. Not a 5+2, but regular 10 speed. Never crawled under it to look at the tag in the short time I owned it, but I do know they made them like that for heavier applications.

 

I know where one is. The tag is missing. The man would part it out for good money. Truck serial number might tell what it is but do not know it it is original.

 

Some transmissions do not shift easily at higher RPM. You have to learn how to work around that.
Some later S model DT's came with a straight 7 speed Spicer. They were OD in high and shifted like a 1 ton as best I remember.

 

Been 20 years since I had mine, but seems like I remember it not liking to float the gears. Think I ended up double clutching most of the time.

 

Why do you care if it is a 14, 15 or 16 series? They will all work if you can bolt them up.
Then you need a different flywheel, clutch, clutch core charge, shorten driveshaft, search for yokes for trans and probably front diff. , change the whole front driveshaft, different top plate to get the shifter through the hole? That is off to a good start.
If $500 is make or break you need to walk on!

 

can you get a bearing that will fit the input shaft and bore the flywheel?