Can somebody advise me on what to do here?
Lawyer up... potentially sue the LLC. Anything else probably puts you in a worse situation.
As I already wrote, there are probably 2 ways to look at a mining contract:
1) You're paying money and getting money back (progagbly Giga's lawyer's pov) - this means you're earning interest on an investment etc.
2) You're paying money and getting a service back (hashing work converted to Bitcoin) - similar to any contract that sells computation power (like render farms).
Probably nobody knows which of these 2 will hold in front of a court (even the "you're paying money" is debatable, if Bitocin are not money in the first place), the worse case of these 2 is of course case 1), where Giga nearly operates a bank/money printing operation from a legal pov. To decide definitively you need to lawyer up, drag Giga's LLC to court and you'll probably settle this out of court, since it's much cheaper to just pay you whatever you want to have for the 40 shares than to risk having to pay all "bond"holders if the court really makes a decision.
There will be a LOT of people not jumping through these regulations and just writing the few shares off, so Giga can probably easily pay his lawyer from the money you threw at him.
OR
You can just fill out the form, send in the information and start getting your dividends. On this path you will:
1) Have to trust his attorney to keep your information private and secure.
2) Get a 1099 (or other form if you are not in the US) at the end of the year which will contain the dollar value of all BTC sent to you, valued at the time they were sent.
3) Since you get a 1099 (or other form) it will be up to you to report this on your income tax form
4) I personally believe that the GIGAMINING share are now worth zero as (so far anyway) there is no method to sell or transfer them to anyone else
5) Therefore you could probably write off the entire (USD equivalent) amount you used to buy the shares - this would offset any 1099 income and will probably give you a net loss on your taxes
On the last point you should concur with someone that knows what they are talking about I am not a tax guru.