As a preliminary remark, the subjunctive I is rarely used in spoken German. Usually you will only find it in written German where it is primarily used for indirect speech.
The subjunctive I also has the problem that with most verbs in the first person there is no difference between the subjunctive I and the indicative. In these cases it is usually replaced by the subjunctive II.
If you use "Ich werde" the subjunctive I is indistinguishable from the indicative. So what you actually get is the future tense ("I will sleep") which is not a good choice if you want to express a wish.
"Ich würde gerne" is a common phrase when one wants to express a wish. Today "würde" is often used instead of the subjunctive II:
Ich schliefe, wenn es nicht so laut wäre
Possible, but rather old-fashioned. What you would hear today is:
Ich würde schlafen, wenn es nicht so laut wäre.