Figure 1. (a) 2-wire and (b) 3-wire. Source: copied from my answer to Several Questions About Analog Input.
... but if I can have non isolated power provided externally can I tie my 3 wire signal line to the + terminal on the 2 wire controller and tie ground to the - terminal?
Yes. Consider Figure 1b. The 24 V supply is feeding the 3-wire transmitter while the grounds are connected. The 24 V could be supplied from the receiver panel or could be supplied locally at the transmitter.
As an aside, the 250 Ω resistor shown in the receiver is the typical way to convert the mA signal to a 1 to 5 V signal for the internal ADC.
Figure 2. OP's schematic.
You have placed the 250 Ω current sensing resistor in the high side of your device. That means they can't share a common ground.
One of my users has a 2-wire 4 - 20 mA meter, and I am unsure what the normal approach to 2-wire 4 - 20 is.
Can i plug my probe into the user's controller? If so what wires go where?
You can provided the user's meter is not grounded. If it is you will have a short across the transistor and lower resistor - always give designations to components on schematics - resulting in 20 V DC applied across the 250 Ω resistor which will pass 80 mA.
Your configuration is unusual and this could give rise to problems on installation.