I've cleaned up after lightning hits an antenna, and designed spark gaps to protect electronics. The last thing I'd do is install a lightning rod through my basement. That stuff should stay outside, irrespective of NEC 810.21(J). Ground loops are not a serious concern in this particular application.
I'd also consider changing the 8' rod into two 4' rods, which are far easier and safer to drive into the ground.
At the shed
Grounding Electrode
The first thing you'll need to do, is to install an approved grounding electrode at the shed. For this answer, I'll assume a 5/8" x 8' grounding rod will be installed.
Bond the Mast
You'll have to bond the mast of the antenna to the newly installed grounding rod, which you'll do using a 10 AWG copper conductor. You'll attach the #10 conductor to the ground rod, using a fitting approved for the purpose. This fitting is only allowed to attach this single wire to the rod, so you can't use it to attach multiple wires.
Bonding the Electrodes
A bonding jumper of not less than 6 AWG copper (or equivalent) should be connected between this new ground rod, and the grounding electrode of the house.
Grounding the Cable
You'll want to run a coaxial cable with a built-in ground wire, from the antenna to the house. Otherwise you'll have to pull a 10 AWG grounding conductor along with the cable.
At the House
Connect the Cable
The coaxial cable should be attached to an approved Antenna Discharge Unit, before it enters the house.
NOTE: When shopping for an Antenna Discharge Unit, you'll want to look for a device that is listed to comply with ANSI/UL 452 "Antenna - Discharge Units".
Grounding
How the cable and ADU are grounded, completely depends on your grounding system. I'll cover two common methods, which should give you a good idea of how to handle it.
Intersystem Bonding Termination
The easiest method, is if your house has an Intersystem Bonding Termination. This is typically a terminal affixed to the outside of the service equipment enclosure, or a terminal on the outside of the house that is connected to the service equipment. In this case, you'll simply attach the ADU and cable grounding conductor to the IBT.
Grounding Electrode
If there is no IBT, you can connect the grounding conductors to the grounding electrode at the house.
No Intersystem Bonding Termination or Grounding Electrode
If your house is really old, you might have neither an Intersystem Bonding Termination, nor a Grounding Electrode. In this case, you can use any of the approved grounding electrodes described in the National Electrical Code article 250.52.
Best Answer
If the conduit is metal, and penetrates the ground it is, by definition, grounded.
But you can also just go buy a grounding rod at Home Depot as well if you'd prefer to do it that way. It's just a copper rod you pound into the ground and attach a copper ground wire too.
You can also ground it inside via the coax. This is how most satellite dishes are grounded. Inside the house there's a groundable coax coupler. Coax goes in one end and out the other, and then the coupler, itself, is connected to a ground inside the house (typically conduit, plumbing or a ground in a junction box).
All that said, would this be the highest metallic element on your house? If not, I don't know that grounding is really necessary. EDIT: it looks like, upon further digging, all antennas are required to be grounded per code.