I can only tell you about how I did mine, which was a Private (Guest) Visa, not a tourist visa.
The dates must match. In other words, for my dates:
Date of arrival and departure: 03/07/2025 - 02/07/2028 that is asked on the visa application is also
Date of arrival and departure: 03/07/2025 - 02/07/2028 that is shown on the invitation letter.
You can enter Russia at any time in the 3-year window.
What sounds strange to me is you say this: "To do this, we would choose a multiple entry 30-day visa for the i-visa invitation." I'm not sure why you say to apply for a 30-day visa if you intend to get a 3-year visa. Maybe it is something to do with the company you are using to apply.
The invitation letter - passport control won't usually deal with that. They will not ask for it nor will they check it. You can have a copy with you want. But the invitation letter is just something you need in order to GET the visa. They will also print out the migration card for you, you will not have to fill that out. My understanding is that at one time, we had to fill them out. But now the passport control does all of that for you.
If it is a Private Visa you might want to do what I did - make an appointment at a Russian Consulate and submit there directly. The application is all online and then you print it out. If you give them a prepaid priority mail envelope, they will mail back your passports to you when the visa is ready. I chose Houston Consulate. Each consulate can have a bit different rules so do the research if you go that route.
Good luck.