Using a vacuum hand pump is the ideal cost affective approach. Downpipes should be off so you can feel the flapper itself go to zero lash against the valve seat when applying vacuum, but you maybe able to accomplish it "close enough" by feeling the lack of "lash" in the wastegate lever itself. That is your call to make.
Essentially you vacuum pump the wastegate actuator to approx. 5.5in/Hg as you feel the play decrease to nearly nothing between the flapper and the housing seat. Once you get to 6in/Hg, there should be no lash and there should be some "resistance" in rotating the flapper as it sits on the seat of the turbine housing. Doing the test several times after adjustment helps get the feel of it and also confirm your results of adjustment. I try to aim for no play and some resistance in turning the flapper around 5.8-5.9in/Hg, and start to feel a little play to no play around 5.6-5.7in/Hg. By 5.5in/Hg the play should be fairly evident. You want to adjust both turbos using the same method. This procedure is something I semi reverse engineered from the BMW TIS, and from bench testing many sets of turbo take offs. If you can find anything better, or seemingly more accurate, let me know because from what I have seen there's not much out there.
About Wastegate Rattle.
First off, every component in these Internal Wastegates wear out. They are JUNK after some mileage.
1) The Flapper is where I believe alot of the more renouned rattle takes place, as it can resonate against the turbine housing seat when its lightly seated or also as it spins while open from the exhaust gas pulses. The clearances in the flapper to the wastegate arm seem to always be VERY worn out, when manually spinning on axis by hand you can hear it rattle as it rotates/flops around.
2) The wastegate arm and internal bushing. These too become very sloppy over time. I believe they can cause some rattle as well, but I dont believe it's as noted as the flapper above. The bushing and arm DO wear significantly though and usually end up binding, which can cause the wastegate arm travel to degrade and perform poorly. It also can cause the flapper to not close all the way which can lead to more rattle. The excess clearances in this area due to wear require further adjustment to the actuator rod. This is why the dealers try to usually adjust the actuators (or replace/adjust them) initially. That is to shorten the rod, making up for the slop in the worn bushing, and allowing the flapper to seat under the defined amount of vacuum. This will buy some time, but certainly does not fix the problem.
3) The Actuator Rod End to Wastegate Lever Pin. This is the part you believe is causing the rattle in your car. I am sure it does contribute to some rattling, but certainly is not all of it. If this is what you are trying to counter, for now, I'd recommend a low load disc spring washer. I haven't tried them myself yet, but I have found a couple sizes I believe would work perfectly to remedy this area of the rattling.
4) All components. Even new there are clearances in these components. Some rattle (a very tiny amount) is somewhat normal. But its when things begin to wear, it becomes intolerable, and they are very prone to wearing all throughout.
I’ve been doing my research. Haha! 
