Just to kick around the solar trickle charge idea a little. It isn't really feasible to trickle charge a high voltage battery. To do so, you'd need to generate hundreds of DC Volts, and there isn't really a mechanism for a Tesla to DC charge without a Tesla Supercharger (which has communication protocols, etc.). The Tesla isn't like a low voltage golf cart. Either the Tesla is actively charging (on AC power) or it's not, and when it is, it's probably a minimum of 5 Amps at 120V = 600 W. So either the solar would have to generate at least 600W (e.g. 2 residential-sized panels), or you would use a 12V car-type battery as an intermediate (solar to charge controller, which charges 12VDC battery, battery powers 120VAC inverter, inverter charges the Tesla). I think generally inverters don't like being connected directly to solar without a battery in between to buffer current spikes. Also, without an intermediate battery, any cloud would reduce DC voltage below the inverter minimum, shut down the inverter and disrupt charging.
That said, you'd probably want at least a 1000 W inverter. The problem is that if the inverter is ON continuously (e.g. overnight, through stormy days, long winter nights), it will probably drain the 12V battery to nothing, even when you aren't really using the 12V battery & inverter to charge the car. Another problem is that while you can manually (remotely) set the car to charge during daylight hours via the app, you probably can't remotely turn on the inverter. Inverters tend to have manual power switches, and you won't be there to turn it on.
All this is pretty fragile, fidgety, and unreliable. Are you sure you're not within range of a 120VAC outlet with access to a properly rated extension cord?