Let me provide some feedback / observations I have gathered from talking to other owners of Model Y's
Your estimate on the price of 20" tires is in range - $330 to $400 each. The current market price for 20" " new Tesla induction n Rims is approximately $330 each...so rough numbers for OEM induction rims and tires = +$2600 (that does not include shipping, balancing and Tire Pressure Monitoring valve stems). While I am sure many go this route or buy non- OEM / Tesla Rims and Tires , most of the Tesla owners I communicated with simply look for "take offs", meaning Tesla owners that want to install other rim / tire packages...... you can find those on this site, craigslist, ebay & others. What I have seen over the last 30 days is Tesla owners willing to sell low mileage (500 or less mile) "take offs" - for $2500 to $3200. Basically new Induction Rims and Tires.
Additional background:
Gemini 19 inch rims are the most durable
Induction 20" Rims and Tires - provide better handling and a more sporty feel.
Uberturbines 21"Rim and Tires - which come on the performance model are amazing and designed for performance - stiff / firm ride
You will see many Uberturbine packages for sale as "take offs" - the feedback is that they are for the performance minded driver, best in class.........but as you may expect not a good match for city driving or areas with rough pavement.
20" Inductions seem to be performance minded - best of both worlds??
19" Gemini --- best all round package -less fun, but more durable. Rub a curb, no problem - new wheel cover is $35.If you dont like the looks of the wheel covers, pull them off - there is a cool ally wheel behind. You can purchase a set of lug nut covers and center caps for under $100 on the Tesla site. Best package for extending range . I have heard estimates of 2 to 5%?
Hope this helps.
Other with more experience or with data driven fact bases can provide better guidance.