You can use a foot switch to control the motor on the 1617, but having the switch on the handle is really nice. So if you don't replace the 13 and use it for freehand cuts, then you can just get a Triton TRA001 for the table. It is its own lift and 3.25 hp, and costs less than the cost of the lift you're considering. If you want to see a Triton in action, look up YouTube How-To videos by Marc Sommerfeld showing how he builds things. He has a Triton under that table of his, so you can see how it really works. Remember that he removes all safety devices so the camera can follow the action. Leave your safety stuff on.
You should be able to use your existing mounting plate, but may have to drill a hole for the above table crank, which comes with the router. You could use the Triton freehand, but as I age, it's just too heavy for me to safely handle freehand.
One more minor thing, at some point your 13 will need new brushes, so don't be too quick to abandon it. It is clearly a good machine.