At least OP has the sense to lay out the scenario, not just to himself, but to the board. Kudos for that!
Reason 1: This is really just something you either need to deal with, or yes downgrade your car. With no tracks around, you're not going to really stretch the legs on your car without throwing in a lot of risk (risk of accident, risk of driving record hit...). What you should do, should you keep the Z, is do whatever you can to make the Z give you happiness at legal and safe speeds. Swap out the exhaust, tint the windows so the ricer boys can't see your pained expression when they want to race you and you don't. If you love the car at sane speeds, you may have a reduced need to flog the car insensibly.
Failing that, or failing your ability to come to terms with your competitiveness, then downgrade the car. (Also keep in mind, 90% of the cars who bait you are doing so because your car IS better anyway; it's faster, cooler; sexier; more exotic, etc. Any car that IS better, probably doesn't need to prove it to you at a random stoplight.)
Reason 2: Your house is going to be your biggest purchase of your life. And your girlfriend your second biggest commmitment (related to the first: kids). Don't go into it scraping the bottom of your budget if you have a choice. (I'd also suggest not going into it because of others, such as feeling pressured to purchase a deceased family member's house, which I'd personally be a little annoyed about...but that's not for me to judge you on!
) Having your own house, depending on the condition and included amenities, can be very expensive beyond what the mortgage is, especially those first few years as you need to outfit it and acquire the tooling to maintain it.
Keep in mind having a house also means needing cargo space. Bringing home a lawn mower? Snowblower? Furniture? Not in the Z! Or the Versa!
I'd love if people kept their Z as it's such a beautiful car. But life is different for us all, so do what you need to do to maximize your overall happiness in this life.
Usually that means not living beyond your means and also putting practicality just a little bit ahead of impractical fun!
You can have your fun after the necessities are met. Honestly, your job reasons (commute, requirements) really make it sound like you need a snow-friendly vehicle.
Keep the Versa. Get a used SUV for the practicality. And maybe use the difference from a used SUV vs a new SUV down the road a ways to get a used fun car to flog around like an S2000.
(I'm projecting a bit on that last paragraph, as I kinda think that's what I'll do after I'm done with the Z in 5-10 years.)