As the HT's are undermanned, generally you could fly as much as you wanted up to the maximum 960 hours in a year or 100 hours in a rolling 30 day block (my best was 104.5 hours in a 31 day month). The limiting factors would be lack of SNA input from the VT's, mx issues and wx issues. If your goal is to fly medevac, oil rigs, or for the government, it is a legitimate way of not only building a copious amount of flight time, but also to build large amounts of instrument or NVG time depending on how you want your resume to read.
However if your goal is to go airlines, you are better off trying for the VT's - but the regionals are hurting bad for pilots so you will be able to go that route anyway.
While at Whiting, you may want to knock out your multi-engine fixed wing to add on to your ratings. Likewise, make sure to upgrade your commercial helicopter rating to an ATP. You will know the Jetranger inside and out as well as your instrument skills being at their peak so as an IP in the training command is the perfect time to get the top rating.