Last year I had several discussions with Glenn at Palmers about just such a modification. Basically youre asking a single 1/4" connection out of the Tippy valve to handle a potential load and a half. In the event you took a fall and the Satbilizer got smacked that little 1/4" connection is going to get tweaked royally. Probably tear the threads out of the valve and Voila!, time for a new valve.
Now, having said that, we discussed an alterrnate approach but frankly I think it has the same inherent risks as the other:
Instead of using the direct regulator, like you have pictured, one would plumb one of their Vertical ASA adapters like this
or this one
onto your tippy and use their male ASA Stabilizer. These adaptors are used on Autocockers like the older Mini's that don't have an ASA on the body, simply a 1/4" NPT threaded opening.
The reasoning behind this approach being better, I guess, is that that the ASA adaptor would help provide some additional beef to the connections to the valve. By fitting the adaptor snug against the frame of the gun you would and provide a more secure Stabilizer connection point that is less likely to transfer shock up to the threads in the valve.
You would need to use a 1/4" male nipple into the Tippy valve then add a 1/4" female/ female coupling to get a threaded connection out of the body of the 98. (The inline you have shown doesnt have enough thread to reach all the way back up to the valve) Finally you would thread on one of the the Vertical adaptors I've shown shown. You would then use a male Palmer ASA Stabilizer.
If youre dead set on the design you chose simply thread the valve with a male 1/4" nipple and a female/ female 1/4" coupling to get the threaded extension you'll need and then stick your diect into that. It proabably will stick out lower from the body than you want and not look as clean as what you have sketched.
Look at the Palmers Web site under Autococker parts for the component I showed you. If youre serious about this I'd call them and talk with them directly. The price of the phone call is worth the headache and aggravation a ripped out vavle would cause you. But they'll probably understand that you would want to do it any way they just dont want you coming back at them saying they didnt warn you.