The parallel install idea is a nice one, but I can see a problem straight away that MA 4.5 - the agent used in ePO 4.5 can't be used in ePO 3.6.1
That alone might knock your plan for six immediately i'm afraid.
Please take a look at a couple of support articles:
KB51573 lists the supported environments for the various agents.
KB51569 lists the same for ePO.
Well worth double-checking both, they are updated regularly.
The policy models between ePO 3.6.1 and 4.5 are very different too which could make manual policy migration interesting.
Providing you're on ePO 3.6.1 Patch 4 or later the ePO 4.5 installer should recognise and upgrade as appropriate, taking care of most of the work for you.
There's a section in the ePO 4.5 install guide about this scenario.
Perhaps others on the forum who have done this already can share their experiences and offer alternatives ?
~ Actually I'll correct myself there having just set up a clean ePO 4.5 installation for testing purposes. The default agent on ePO 4.5 out of the box is MA 4.0, not 4.5
So if I upgrade from 4.0 to 4.5 the framework agent is the same?