The question involves different aspects
1. Understanding the properties of SPICE tline model
It's an ideal component with partly counter-intuitive behaviour. It has infinite common mode impedance and thus isolates ports from each other. Loading the component with common mode current has effects that will be never observed with a real transmission line.
A usefull approach is to consider it as building block for transmission line circuits. If your circuit involves common mode waves, they have to be modelled separately.
2. Floating SPICE nodes
Floating nodes cause simulation failure in some cases. Adding high ohmic resistors is a possible fix, you can also use the global gshunt option, see Ltspice help or a SPICE text book for details. In this case, the problem is brought up by tline infinite common mode impedance, but it isn't specifically related to transmission lines.
3. Which circuit problem do you want to model?
In the given circuit, transmission line port 2 has no common mode load, therefore different grounding of the port has no effect as long as you are measuring port 2 differential voltage instead of port 2 nodes against ground.
See below test with variable load between port 2+ and ground. => The setup models in no way a "realistic" ground.
4. SPICE can only simulate lumped circuits and some ideal distributed components
Consider that the behaviour of an asymmetrical transmission line, e.g. coax cable, depends on circuit geometry. Presume T1 represents 10 m of RG58 coax cable. Is it coiled up or layed straight on the ground, with which distance? Common mode impedance respectively "realistic" ground impedance seen by port 2 will be different in each case. Finally common mode impedance is coupled to free space, part of the wave will radiated.
A simulation model of 10 m straight coax cable with common mode impedance could look like below. Notice that common mode wave propagation speed is higher due to air dielectricum.