My head's a bit dizzy, so I'm just going to write something off the top of my head without thinking too hard.
Literal
Head [subject-が] dizzily-doing [because-ので], deeply think-not-[without-ずに] half-baked thing [object-を] try-writing.
Blog diary register. 頭がくらくらする 'head spins, feels dizzy' uses the mimetic くらくら for a swaying/spinning sensation. ~ずに is a classical/written negative connective 'without doing X,' paralleling the more colloquial ~ないで. いい加減 has split meanings — literally 'good degree' but colloquially 'half-baked, sloppy, irresponsible' (context distinguishes). ~てみる 'try to V, do V and see what happens' marks the writing as tentative/exploratory.