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Incidentally, the EPO does not allow claiming priority from an industrial design for a European patent application. EPO Guidelines for Examination, F-VI, 1.3, quoting decision J15/80. Points 7-11 of that decision discuss the meaning of Article 4 of the Paris Convention in some detail.
Will this 'later' amendment change the date of my 'now' claims to the date of my 'later' claims?No. Once your PCT application has received an international filing date, that date isn't altered by any amendment you make, e.g. under Articles 19 or 34 PCT. (Except if you're using the mechanism of Rules 20.3, 20.5 and 20.6 PCT, but these are really a stopgap measure in the event your PCT application is incomplete.) As Maca stated, the real issue is that in some jurisdictions, you could have trouble convincing the examiner that your amended claims are properly supported in the description.