There's some research that shows fragment length doesn't have any major effect on MiSeq sequencing. It's not the main focus of the study linked, but they do address it, and find that there is no systemic bias associated with different template sizes (unlike 454, where there was a clear bias towards smaller fragments).

You could contact the authors directly if you want more information.

Article A flexible and economical barcoding approach for highly mult...

You will have some problems if the number of cycles were smaller than the fragment length because R1 and R2 will not reach each other. If you chose go for a single end, check quality at the end of the read, its drops considerably. For 550 bp the kit V3 with  600 cycles could be a better way

if you took the lengh of your fragments into account when quantifying your libraries (kapa quantification for example, see their protocol online) there should be little to no bias towards the shorter ones for this amoutn of difference. As others said you will have to use the 2x300 V3 if you want full size for your 18s amplicon. If you were running independently the two fragments you would have to adapt the concentration of your libraries to accomodate for different sizes as clustering is influenced by this parameter. For your sizes it is regular concentrations from standard illumina protocol. 

Hi. I was wondering if you ended up running the experiment multiplexing both regions and what were your results? I am planning a similar experiment and would like to hear your experience. From previous experience, you want to minimize the difference in bp given that smaller fragments will be preferentially sequenced.