Just block posting by them on most of the boards.
In other word you are saying to close new registrations

Curious to know which boards should be open for them

By the way OP, the post really make sense. If we can control (apply manual review) newbie and Jr.Member's post then a lot of this spamming issue will be resolved.
With limiting the number of posts which Newbie(i think Jr.members need to be in this group) can post daily, it is necessary to get approval for each post before publishing. So it can't be published any post without approving from forum moderators. Yes there can be a problem it is a lot of job for forum admins and mods, but this can be facilitated if more members are included in the moderation.
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Allowed posts going to be published, denied going to trash. Accounts with 30 posts and 90% denied posts going to be banned(numbers and percents is just for example)
x post with y% denied also a good idea IMO. This way the poster will think twice before posting garbage.