There are a number of alternatives. One is to stay on 81 north to I-581 (exit 59). 581 will take you around the southern side of Harrisburg to I-83 north. I-83 rejoins 81 about MM70. However, this has been major backups and accidents since the closure. Alternate two is like you said, I-76 (PA turnpike) from exit 52. Leave the turnpike at Exit 247 which will take you to I-83 as above. Less traffic, but toll road.
PennDot is planning to reopen northbound I-81 next week, but will be subject to frequent closures as the two overpasses are torn down. Reconstruction of these overpasses will take months (the bridge near my house was recently closed to rebuild. PennDot said it will take two years!!!). By June, for your trip, I trust things will be calmed down. Unfortunately, this area of 81 has been under reconstruction for two years already, so this just compounds the problem. Lane closures, cattle shoots, terrible! Good Luck. Will post updates.
Bob & Deb K.
2012 Itasca Ellipse QD 'Elli'
2010 Buick Enclave AWD Toad 'Ginny'