If you want to do co2 in a small operation, personally, I would just go the tank route. After the initial investment, it costs me about $50 a grow (my prices just went up) I don't use it during veg, just flower. I veg for a while so I don't want to waste the co2, nor do I need faster growth during veg (I'm already hydro) If you don't want to refill during your flower cycle, you will want a 50lb tank.
I will also monitor the plants a couple weeks away from due date. Co2, ime, makes the flowering time significantly longer. Which can sometimes work to your benefit, but with finicky strains I sometimes have to shut it off two weeks out of expected date, due to fox tailing or other undesirable traits. Sometimes, the tank just runs out at about 8 weeks anyway so I'll leave it.
But, no, I would not be messing with dry ice to augment co2. If you are large get a burner, small - get a tank. Put it on a timer & be done with it. Co2 should be cycled from what I have read. You don't want a constant flow, you want to fill & let the plants deplete, repeat. The instructions that came with my regulator say it's best if you can fill within 8-15 minutes. So every hour, it kicks on for 15 minutes & knocks it up to 1500ppm. The plants will then drop that to between 800-1,000 ppm, & the cycle starts again. I don't know if that is how everyone does it, but the 3 best growers I know (top notch) all do it this way.
I'm sure it would be a pain, constantly cycling dry ice every hour.
If it matters, in tests that I have done, as scientifically accurate as I can do, co2 increases my yields by about 20% on average, & just better bud compared to when I do not use it. It also makes the heat & humidity that I run at work for the plants. I have to run higher temps/humidity in flower than most. 85-90. Humidity I can alter more easily, but I find most of the strains I've tried do better at 55-60% RH. But I also avoid strains known for bud rot.