Hi Brian,
I did years ago a lot of resin casting. Like you I used a tool to fill the small corners in the mold (tipically the rivets) before pouring the rest. Bubbles were never a problem. Few months ago I did some new castings but could get only a resing with a shorter pot life. I tried to shake it less, as I had less pot time, and I got bubbles and even some areas where the resin was not completely cured, probably due to insufficient mixing. I mean, perhaps your less shaking is counterproductive.
On the other hand in my older trials I also did sudder bubbles with the resin batches older than one year. Bubbles development in the mould while hardening, and more volume contraction. Check your resin shelf life if possible.
Hope that helps.
Nacho