Can a chin-up bar be supported by just two of the four intended mounting points?

Question

I would like to hang a chin-up bar on a drywall.

So far I'm lucky. I measured that the studs (dotted in the image) are 16″ apart.

The distance between the two lower holes in the frame (grey area in the image) are also 16″ apart.

But the two top screws are problematic.

Possible solutions:

1. Don't bolt the top two support points. Two 3/8″ bolts are plenty for supporting an average adult.
2. Use butterfly drywall anchors for the top two holes. They will not take much weight, but they'll at least provide a bit of stability in case someone decides to swing.
3. Neither (1) nor (2) is good enough. Cut out 3/4″ plywood about 18″ ✕ 18″. Bolt the plywood to the wall with four serious bolts, and then bolt the chin-up frame to the plywood (how? And will 3/4″ maple plywood be strong enough?).

Which would you use, solution 1, 2, or 3?

Update

Let me add a second diagram that illustrates how the weight is transferred.

Notice in particular that the frame consists, as is common, of a diagonal support that takes the load to the wall through compression.

This means that omitting to add lumber underneath the bottom part of the structure will result in either:

• if the lightly shaded U-shaped metal part is too weak, it will bend, or,
• if that part is quite rigid, the two bolts at the top will be subjected to an undue pulling (tension) force and that tension—likely equal to the full-weight of a (possibly swinging) adult underneath—will have to go through a single piece of two-by-four (the top one). Remember that there are no studs directly behind the two top bolts.

This means that in addition to the two pieces of lumber suggested in isherwood's solution, it may be necessary to add a third piece of lumber. That third piece need only be glued to the wall.

Which would you do? Would you:

4. Add a third piece of lumber, perhaps by just minimally gluing it to the wall, just enough for it to stay where it is,
5. Add two pieces of lumber vertically such that they cover the width from A to C, or,
6. Add a single piece of (plywood, perhaps) that acts as support for the entire frame?

Update 2

I'm giving up putting in all the details in one question. I posted a sequel here.

Answer 1

#1 relies on the unknown integrity of this device when supported by only the two lower screws. It may not be designed to do that.

#2 doesn't offer anything at all. While hollow-wall anchors can carry quite a bit of weight, it's static weight. The jumping, jostling loads of gym equipment will make mush of your wall. They'll eventually tear out, possibly at an inopportune time.

#3 (or a variation of it using two-by lumber) is the only viable option. I'd probably run three 2x6 boards over your studs with two 3/8" x 5" lag screws at each connection and mount to those. These would be arranged behind each set of mounting points and at the bottom of the device. This approach essentially eliminates undue compression on the drywall--mounting directly to drywall, even with framing behind, risks making mush out of it over time. I would use a router to put a substantial radius on all edges, and then I'd stain and varnish to suit.

An illustration of this solution was provided by Sam. The third board mentioned above is not shown as new information has been added to the question since it was drawn.