Is it possible to do Asthi Visarjan at both Puri and Prayagraj?

Yes, and some Odia families do exactly this. There is no scriptural prohibition on performing Asthi Visarjan at more than one tirtha — in fact, the Dharma Sindhu notes that if a family is unsure which sacred site is most appropriate, they may divide the ashes and perform the immersion at multiple locations. In practice, many families divide the asthi kalash: a portion is immersed at Puri under the gaze of Lord Jagannath for the Vaishnava blessing, and the remainder is brought to Triveni Sangam, Prayagraj for the highest Puranic merit. The two immersions complement rather than duplicate each other. If travel is a constraint, the courier service offered by Prayag Pandits allows the remaining ashes to be sent to Prayagraj and immersed on the family behalf, with video documentation sent after the ritual.