Here’s the overview and the Carver MTB component:
Here’s the section from the NE end of Battle Creek (technically NE end is not in park, it's Scenic Overlook)
The area circled in red is where I’d prefer to jump out of BC onto the paved trail. This is at the base of Goat Trail (not a beginner trail!), from the satellite map close up it looks like one could descend a grassy area to the paved trails (see footnote ). The map below is from mtbproject (REI).
This would be a solid day of road/single track riding for most of us!
Update 6/9/2019 - more detailed version for a Sunday Ride
Depending on our timing a few segments can be dropped. There aren't a lot of places to stop and eat until the end of the trail. This ended up being a bit over 30 miles but it felt like 50-60 riding my mountain bike, doing the trails, and a surprising amount of up and down.
Segment 1: Groveland Tap to Overlook 8 miles
Segment 2: Batttle Creek Overlook to exit point (mtbproject)
The red line is the path overlaid on the mtbproject map. I think this is probably about 5 miles. The exit, is as above, not official. Will be bushwhacking (see footnote ).
Segment 3: Exploring a curious neighborhood (2.7 miles)
This is St Paul East Side. The "Boys Totem Town" is a 100yo correctional facility for youth. It is to close in July 2019. (When we rode this in Strava you can see where we took a wrong turn or two.)
Segment 4: From start of Battle Creek back to the trails
The lower right quadrant here are trails we ski in Winter. This segment also appeared in an earlier post. The top right quadrant is Battle Creek Water Park, there can be ice cream trucks there and there are bathrooms. From here you can see wetlands Battle Creek runs through, but it starts in Battle Creek Lake in Woodbury (I think it is underground until it emerges near the water park).
When we actually rode this (Strava, below) we missed turning left on Upper Afton Road so instead of taking Battle Creek Road to the trails we followed Creek back to Luge Connector. (Battle Creek goes underground again at the end of the park to pass beneath rail and freeway.)
Segment 5: From S Battle Creek Road pick up the trail to Bowl and Luge to Overlook
8.3miles, 55 minutes. There are many eating options here at the end.
And here's how it looked on Strava with a few false turns, about 30 miles (felt longer):
 We were able to transition from the segment of Goat to the paved bike path -- but it's not easy. There's only one place to transition and it's fairly steep. We were able to walk it down using the bike partly as an aide -- but only because invasive vegetation had been cleared and it was opened up a bit.