If you accept that you're maximizing expected utility, then you should draw the first card, and all future cards. It doesn't matter what terms your utility function includes.

Note however, that there is no particular reason that one needs to maximise expected utilons.

The standard axioms for choice under uncertainty imply only that consistent choices over gambles can be represented as maximizing the expectation of some function that maps world histories into the reals. This function is conventionally called a utility function. However, if (as here) you already have another function that maps world histories into the reals, and happen to have called this a utility function as well, this does not imply that your two utility functions (which you've derived in completely different ways and for completely different purposes) need to be the same function. In general (and as I've I've tried, with varying degrees of success to point out elsewhere) the utility function describing your choices over gambles can be any positive monotonic transform of the latter, and you will still comply with the Savage-vNM-Marschak axioms.

All of which is to say that you don't actually have to draw the first card if you are sufficiently risk averse over utilons (at least as I understand Psychohistorian to have defined the term).