Based on the 248 HV requirement, it seems you might be working with the NACE MR0103/Rp0472. Definitely want the 200F preheat, high interpass temperature and temperbead as suggested. We have changes to ER70S-3 for the weld metal as well, however, it doesn't seemlike that might be your issue. Make sure your final passes are not flush with the surface of the test block. You should run at least one extra layer and maybe two making sure the toe of your temperbeads are not more than 1/16" from the edge of the welds touching the base material. This will temper the HAZ in the cap pass most of the time. ASME Section IX-07 has a good diagram of temperbead welding in section 462.12.
Another thing you may want to consider is that not all heats of 516 Gr 70 are equal and if it contains residual or intentionally added elements such as Cb, V, and Ti you may face some difficulties. NACE SP0472 and NACE 8X194 have good information on base material chemistry. One last suggestion would be to weld your test plate and cut one section to send to the lab first for a hardness traverse. If you encounter a problem, you still have the rest of your test block to run additional passes or see if a half bead technique is needed vs the temperbead before sending for the final hardenss traverse. I am spoiled here as we have our own lab for Vickers hardness traverses.