I really wish the spider exercise had been better thought out. It seems to be a common issue that new players struggle and think their fingers are too short, or that they struggle with the stretch required.

Try starting from higher up the neck. 7th or 9th fret instead of the first (or even 12th fret), then try lower down the neck after a week or so. As for looking for a guitar with a shorter neck, the difference is only quarter of an inch, so it won't solve your problem.