When the halfer argument says "Sleeping Beauty receives no new non-self-locating information," it means that SB (their only subject) new she would be wakened, so that provides nothing that can change her assessment of the coin flip result. Yours do get new information, so your variation is comparing different things.
There are several ways to do what you are trying do, that don't have this problem. One is to use four volunteers, instead of their one or your three. Each will be assigned a random number, just like you do, but each will undergo an experiment that is functionally equivalent to the popular version of the problem. The same sleep and amnesia drugs will be used, and each will be awoken at least once, but maybe twice, based on the same fair coin toss. Only their schedules and the question they are asked will differ, but end up being equivalent to the popular problem. On Monday and Tuesday:
#1 Will be awoken unless it is Tuesday, after Heads.
#2 Will be awoken unless it is Tuesday, after Tails.
#3 Will be awoken unless it is Monday, after Heads.
#4 Will be awoken unless it is Monday, after Tails.
Each will be asked for their credence that this is the only time they will be awoken. For #1 and #3, that means credence in Heads. For #2 and #4, it is credence in Tails. For all four, the answer has to be the same as the correct answer to popular version of the Sleeping Beauty Problem.
One each day, we can bring the three awake volunteers together to discuss their answers. The only restriction is that none can know what numbers the others were assigned. Either because none know, or they can't share if they do know. Of these three, exactly one will not be, or was not, awakened on the other day of the experiment. But none of the three can have more, or less, credence that she is that one instead of one of the others.
So with three awake volunteers, one of whom will be awakened only once, the answer is 1/3.
Being awake does not provide any new information about the two-day experiment as a whole. But it does provide new information about the half of the experiment that is currently being conducted, that is isolated from the other half by the amnesia drug, and so is the only part of the experiment that a volunteer knows about. This isn't technically "add information," but it does "remove" some information from the knowledge that SB had on Sunday Night. It works the same way on their ability to update.