I can't access that calculation, you need the postcode as well. Don't worry though.

I think that I can spot what may be the issue with your original calculation.
You say your rent is £94 a week, but to get the figure that the calculator gave you I had to use £694 a month.

So is it simply a 'fat finger' typo, and you caught the 6 as well as the 9? Check your calculation for what you have put for rent and if it's weekly/monthly.
£694 would be exceedingly high for weekly rent so the calculator would probably assume it was monhly anyway.

That rent of £94 a week makes a difference, for UC that is calculated as £94 x 52/12 = £407.33 a month.

Which would give you a UC Total of £1882.18 a month.
Adding the CA, CB, and DLA that would be £2857.26 overall.

Both my calculations and Turn2us agree on that.

TBH that is not much difference from what you are getting now, just a couple of quid a month more.

Use CFF-HC4-3Y9, and postcode CA222AE to access that Turn2us calculation.
Take no notice of the postcode or the Council Tax relief figures, I don't know your postcode so just used one at random. (It's in Cumbria).
But any Council Tax relief you do get should be the same under UC as it is now, so as a comparision it still stands.
I've had to make another couple of guesses, (eg. number of bedrooms), but nothing that would change the outcome.