confidence intervals for interpolated values in logistic regression

This isn't a mixed-models issue, so it's not quite on-topic for the
list, but I'll go ahead and give a few hints:

1. Don't do the linear algebra yourself -- use predict(). This is
especially true for GAMs where you need to worry about the smoother
terms (and where the necessary matrices for the linear algebra isn't
immediately obvious from the model summaries). (Also,l you mention GAMs,
but then you don't mention any smoothers .... )

2. I think the functionality you're looking for is more or less the
effects package.

3. There is some fine print on that though: there are confidence
intervals (which summarize your model and its uncertainty and are what
are shown in effects plots) and prediction intervals (which show how
much variability you would expect in new data -- and this is more than
the confidence intervals, which summarize the uncertainty in your
parameters, not total variability).

4. mgcv may have a relevant parametric boostrap method, but I don't
think is what you're looking for. mgcv does have some nice plotting
methods built-in though in addition to the methods in the effects package.

Best,
Phillip