As I see things at the moment the club has 3 options.
1) Appoint somebody long term who we think is able to take the club forward.
2) Appoint somebody until the end of the season with a specific task to keep the club in the Premier.
3) Continue with Unsworth in the role of caretaker manager until they decide on 1 or 2 above.
After what has turned out to be 2 poor choices, I think it is imperative that the board get the right man/men this time to look after the long term interests of Everton. That may also include a new DOF. I think everybody will agree that this has to be our main objective if possible. However, that man/men may not be available at the moment for whatever reason, in which case we need to wait until he is available. This is far from ideal but better than making another wrong choice.
We then have to consider the short term. We can only appoint somebody new if they are currently available, and there is probably a very short list to work from. The new manager (unless Unsworth is given this role) would need to come in and get used to the club and players, and it will probably take months rather than weeks before they start having a noticeable effect. Even then there's at least a 50/50 chance that this could backfire. Unless we can bring in somebody short term of the standing of Ancelotti, I personally see this as a non-starter.
So that leaves us with Unsworth continuing on a temporary basis. I was originally in favour of giving Unsy a chance, but let's be honest he hasn't exactly covered himself in glory so far, which is why I wouldn't confirm him for the rest of the season at this stage. In his favour he knows the club and staff and players. Plus the younger players will have a tremendous amount of respect for him too. It will also be harsh to judge him too severely on his performance so far as he's had a pretty difficult set of games, and hardly any time to work on the players in training with games coming thick and fast. However his team selections and tactics have confused most of us and we seem to have to give up a goal or two before we start playing. Plus I have no idea what has been happening as regards Vlasic, who has been one of the very few positives so far this season.
If the board are unable to bring in the right manager to take us forward as this stage, then I believe the better of two poor options is to run with Unsworth on a caretaker basis, rather than bring in the likes of Allardyce. I have to hope that he will learn from mistakes made so far and that work on the training ground will shore up the defence so we stop conceding cheap goals. I also believe that there is enough quality AND endeavour in the squad, to go on a decent run over the next 8 games where we play 7 teams who are in the bottom 11. I wouldn't be surprised if we were 7/8th by the end of the year and maybe 10 points clear of the relegation places.
In the ideal world we would be able to bring in a manager like Tuchel, or, somebody of his ilk, who will be able to develop the fantastic crop of young players we have at our disposal. Pending this I would rather we run with Unsworth on an ad hoc basis. At least then, if there isn't a turnaround in results (which I don't expect) we can react accordingly.