So, it would take about 3 days to heat up. After that I assume they maintain temperature with a cover fairly easily?
The calculators on this page compute how long it takes to heat water, how much energy is consumed, and how much heating power is required.
bloglocation.com
30 hours for 45 to 100 °F heating for 1000 gallons, 60 hours for 2000 gallons. Not counting heat losses, obviously. There are three calculators on that page. One for how long to heat at a given heat input (kW), how many kWh used to heat, and the third to calculate the size of heater needed to heat in a specific period of time.
Note that at 2000 gallons, heating from 45 °F to 100 °F uses 270 kWh. That's $30 to heat if you pay $0.11/kWh (which is pretty cheap for electric), again not counting heat loss. So consider the size in gallons in your design.
While I fully support DIY projects, I'm curious why you want to DIY a hot tub? Is it cost? Because if not, you can get really nice pre-made tubs with good insulation, lots of jets, and comfortable molded seats. The 6 seat spa that came with our house:
It seems like it would be very difficult and time consuming to DIY the comfort and relaxation that a pre-made, molded hot tub would have.
When we went to the spa store to grab filters, we looked at the ones they had on the floor. There was one that could fit 8 people in comfort, was deeper than mine in the center, for additional legroom, had tons of jets, height adjustable neck jets, etc.
Any natural gas service in your area?
This. If you have natural gas service, use it. Not sure your prices but where I am in the US electric resistive heat is
4.5x more expensive than an 80% efficient natural gas heater. If you have propane that too is likely cheaper than electric, though not by as much. Additionally, both types of gas will allow you to get a bigger heater and heat your large amounts of water in a reasonable time (hours, not days).