Transmission Mount is broken

Ford Crown Victoria Police Interceptor,

https://www.google.com/search?q=%E2%80%8BFord+Crown+Victoria+Police+Interceptor+canister+vent+valve+diagram

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You need to open the hood. You can have someone stand by the fender and look at the engine while you do this test. Now start the engine and put it into drive gear, apply the brake and step on the accelerator pedal to bring the RPM up a little. The helper must watch how much the engine as it lifts or twists. More than an inch or two you have a broken mount. Now do the same thing in reverse gear to check the other side. This vehicle is a rear wheel drive and will have 3 motor mounts. Left , right (both under the exhaust manifolds) and a rear mount at the rear of the transmission. This mount should be visually checked as well. I hope this helps.

basically pull the motor off the mount
if it is broken then the mount will part
inspection will reveal a shiny part of metal where the rubber is rubbing on the steel

I know you had a transmission installed but did you get the tourque converter as well as the transmission ... not all transmission shops will do a great job you need to find someone reliable you can trust ... personal opinion says find an older white guy thats been doing it for years worked well for me

Yes it can, there are many parts around for a rebuild, even upgrade some parts, you can also rebuild your transmission too, even change gears. But you can also find used low mile engines around as well as a replacement , These are modular engines , Grand Marquis will work as well

I can only forewarn you about several things to watch for in hope of providing you with something to prevent you from breaking something.
You must also consider loosening the transmission mounts to free up the entire drivetrain. There may be some clearance problems at the rear of the motor and the Radiator hoses may not stretch, nor may the fixed A/C lines to the front A/C cooler allow much travel space.
The oil pan is not a lifting point, nor is the crankshaft pulley. The exhaust system is not flexible either.
Your best bet is to look at the actual motor mount and see whether the mount is flush or has protruding studs. Flush shaped will be easier to handle. An 1/4 inch of clearance would allow you to slide parts through the opening.
You could still get another Expert to answer. I owned a 1994 Crown Vic and was underneath it many times, but never changed a motor mount on it.

You need to change your cable that goes to your transmission from the odometer easy fix

Let me get this clear.. you did not remove the cross member to drop the pan?? WHY?.. If you broke the bolt loose that is made into the transmission mount.. you need to be able to tighten the mount somehow.. if you can't tighten the mount, yes, you need to replace the mount . NEXT TIME - Use a jack stand under the front of the drive shaft to hold up the transmission.. this will make the job easier!!

MOST INTERCEPTER CARS, MEAN THEY HAVE AN ADDED GEAR IN THE TRANSMISSION! WHAT YOU'LL BE DOING IS GOING TO A TRANSMISSION WITHOUT THAT EXTRA GEAR! TO ANSWER YOUR QUESTION: YES YOU CAN REPLACE IT WITH A REGULAR TRANSMISSION! YOU JUST WON'T BE ABLE TO CHASE BURGLARS! HAHA

It should be doable, if the engine size is compatible to the Transmission mount. You may need to change the Engine mounts location. As far as if it is a good idea or not only you can as the owner can decide that.