In the answer to this question, it's clear that RAW, short rests cannot occurring during a long rest; you have to choose which before you begin.
This question confirms that you can cast spells before the end of a long rest.
The catnap spell description (Xanathar's Guide to Everything, p. 151) states:
You make a calming gesture, and up to three willing creatures of your choice that you can see within range fall unconscious for the spell's duration. The spell ends on a target early if it takes damage or someone uses an action to shake or slap it awake. If a target remains unconscious for the full duration, that target gains the benefit of a short rest, and it can't be affected by this spell again until it finishes a long rest.
Errata has confirmed that a long rest requires at least 6 hours of sleep. so...
Can I circumvent this short rest/long rest exclusivity by casting catnap on my party members and myself before conking out for the full long rest duration?