From what you've written it seems you understand how the major scale shape moves up and down the neck depending on which key you're in.
Think about where the root note of the new key shows up in your original key's scale shape. That note would be a good one to shoot for at the end of your modulation between keys. This will be the root note of your new key---imagine what the scale shape looks like with the root in this new spot.
In the measure before the key change, play the first half of the measure using the original key scale, then in the second half of that measure switch to the shifted scale shape (probably end that measure on the 7 of the new key). Make sure you land on the root right at the key change.
Anyway, just a few thoughts, your mileage may vary.
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