lemon, lime, and bitters sorbet

This one was absolutely melting my brain trying to figure out, especially since I did it without a refractometer. Probably a bit ambitious given my inexperience, but I gave it a go nonetheless!

NOT A RECIPE, BUT MY METHOD:

I freeze-distilled 1.1L lemonade (poured into smallest bowl that could hold it, froze solid, upended frozen bowl onto sieve sitting on 1L measuring cup and let it melt for a day) down to get the syrup. I pulled it at 500mL syrup (approx. 8h after taking it out of the freezer), then freeze-distilled a full LLB (300mL Schweppes lemonade + 30mL lime juice cordial + dash of bitters) for another 160mL of syrup since I felt like it needed a little more. I added 120mL lime juice cordial and a half teaspoon of bitters, plus 100mL water. That 100mL may have been a mistake, but I churned it anyways. It came out half-syrup, half-rock-hard, so I let it melt down and added 220g warm water plus 5g (~1.5tsp) gelatin as that was the only stabilizer-like thing I had in the pantry. This ended up being much better texture wise (though still quite soft when I got it out 5h later to scoop) but I definitely had some trouble with the gelatin, so I think in the batch for the party I'll only do 3.2g (1tsp). The flavor is spot-on, though!

Recipe-ish that I'm planning on using next time:

1.1L+300mL Schweppes lemonade, freeze-distilled to 600ml(ish) syrup

150g lime juice cordial—Schweppes if you can get it but I used Bickfords bc our local colesworths have stopped carrying Schweppes cordials

5/8tsp bitters—we use Convict Bitters but angostura is traditional

3.2g (1tsp) gelatin bloomed in 250mL water

for anyone wishing to offer critique/advice: I am unlikely to source any fancy stabilizers in the next week and a half before I need to make the next batch, so any advice on making the gelatin work properly is welcome! I also have access to glucose syrup, if that helps you with advice-giving.