Mike, I am hosting with A2 and have not had issues that I can recall using Composer, as long as I can remember Composer has worked without alterations. I use Composer with many Mediawiki plugins as well and there has not been any issues. Perhaps A2 has presets on our accounts that are friendly to Composer? I am not sure, but I just thought I chime in here and let ya know A2 shared hosting does not seem to have those issues.
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