I'd put a pedestal on top of each end of the conduit, pull your cable in and put some terminal blocks inside the pedestals to make the transition. Give Schultz Communications a call, they have everything you'll need and the expertise to get you the proper hardware:
SCHULTZ-CAD6 PEDESTAL LINK VARIOUS TERMINAL BLOCKS Here's a picture of an example of using a pedestal closure along with RPT blocks to make a transition that we did recently.
Actually, this was a small-count cross-connect facility (25 pair in, 50 pair out), but it shows the flexibility of using pedestal-type terminals at poles and buildings:
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Here are illustrations of some of Emerson/Reliable's garden terminal pedestals with various blocks installed. I wish we still had these in stock because I'd be happy to provide you with everything you need, but my boss made us throw all of that stuff away:
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