I would suggest using Gibson assembly. I am not an expert but this is the kind of problem that it is designed to solve. Probably there is some way to do this by PCR but I expect that it will be quite finicky.
See this quote from that page (my emphasis):
Tip: “Stitching” Fragments Together using Oligos
When you need intervening sequence between two PCR products, one method is to “stitch” together several oligos. This technique is especially useful for introducing promoters, terminators, and other short sequences into the assembly and is used when the part to be inserted is too long to include on overlapping PCR primers (>60 bp) but too short to make its own part (<150 bp).
Please note that the way to design the “stitching” primers and the amounts of them to include in the Gibson reaction are different than with normal PCR primers. The details are published in ( Nat Methods 2010; 7:901-3 ).
Tip: Number of Fragments Assembled Simultaneously
Multiple fragments can be assembled in one reaction. However, some labs have observed a sharp decrease in success rate when assembling more than 5 fragments at a time.
It looks like there are people who argue both that Gibson is impossible with short fragments or that it works fine. There is more information on this here and here and here. Due to the relatively complex nature of your reaction, I think that Gibson might save you time. But other people linked there do claim that PCR works better.
GaelC's answer above has better/more specific methodological advice on PCR assembly.