Are Proto-Slavic present passive participle forms (e.g., *beromъ) from first-person singular present forms (e.g., *berǫ)?
No, I don't think there's a formal or semantic reason to think so, especially since Slavic -mъ is a perfect cognate with Baltic *-mas of the same meaning (cf. Lithuanian žiūrimas filmas, a film that's being watched), and thematic 1sg. in Baltic languages continues the original PIE *-oh₂, without the Slavic addition of -m.
The origin of this Balto-Slavic *-mas however is not perfectly clear. It's extremely tempting to link it to Greek -μενος and Sanskrit -(m)ānas, with the identical (and not that ubiquitous present (medio)passive) function, especially since the ending also seems to appear far from the closely related Graeco-Aryan dialects, in Tocharian, and in Latin (in two words: alumnus and femina). Unfortunately BS *-mas can't be derived from that ending (which itself poses some problems for reconstruction, but *-mh₁nos and *-menos are a couple of suggestion) without invoking a possible, but ad-hoc simplification mn>m. The fact that a lot more obviously related ending appears in one Old Prussian word (poklausīmanas) if anything only confuses the matter further.