A while back, we had a lengthy discussion of that in here (anyone willing to dig up the link?). I think the consensus was that no one liked it but no one could explain why it was wrong. Many, many years ago, I tried that and the supervising partner said "You can't do that." I haven't tried it since.
I don't like those because courts/PTO may later find them to violate 112, fourth. Every dependent claim must include every limitation of the parent claim. Claim 2 recites a method. Claim 6 is not a method, it is an article of manufacture: the whole point of ~Beauregard claims is to remove them from the "process" category of 101. For example, a method claim requires the infringer to actually perform the method steps, but a claim to a CD-ROM for the method can be infringed
even if the method is never performed. For that reason, claim 6 arguably does not include every limitation of claim 2, and therefore is invalid. See the recent Supplemental Guidelines on 112 (specifically the part about 112, 4) in the Fed. Reg.
I remember hearing that the MPEP is inconsistent about these claims: one section says they are ok, another says not. But I can't confirm or tell you the sections.
I think the multiple dependent form might actually be useful if you need an extra few minutes to get a filing date. I think you can avoid the multiple dependent claim fees by filing a preliminary amendment with the missing parts, but don't quote me on that -- others here know the rules much better than I do.
I liked the multiple-dependent -> preliminary amendment route because it gives you a much broader disclosure while avoiding the additional claim fees. We would routinely receive foreign applications with tons of
multiple dependent claims. A coworker wanted to amend the spec directly. I insisted that we leave the spec untouched and file a prelim - thereby preserving the broader scope of the original claims. Ultimately, we called a name partner after hours and he agreed with me.