Yes. Easily done using a manifold of PVC piping pushing air down into the soil through a series of wells, (8'-10' grid is average). Sample the parts per million hydrocarbons on a monthly basis and plot a graph. Fine tuning with occasional addition of moisture and ammonia vapor will keep the oil eating bacteria happy! 30 ppm is probably sufficient for EPA or local government after removing the leaking tank of source of contaminant.
Actually, the typical preferred method for is vacuum applied, not pressure. Pressure will disperse the vapors away and possible into areas that will cause worse contamination and/or potentially dangerous situations. The preferred process is called Soil Vapor Extraction. A vacuum pump with sufficient vacuum to create movement at about 20-30' radius of influence from a 2" of 4" well is typical. If the soil is clay consistant, count on a PD blower or liquid ring pump for vacuums in the 10"Hg - 25"Hg...For sandy soil, regenerative blowers are tpyical...The range of 30ppm in the soil sounds about right, but it really depends on the State and the local/federal requirements. Google your states Environmental Quality Department and you can usually find the statutory requirements.
Quick answer probably, it really depends on the requirements of your local state. 3700 ppm sounds high, but it isn't 3700ppm of gas it is 3700 ppm of something. The somethings are the key, some regulatory limits can be 1 ppb and even lower, where others 3700 could be acceptable, especially after a risk based study is performed.
There are thousands of types or remediation processes, I have had good success by combining Soil Vapor Extraction and Air Sparging (basically what the first responder recommended). Right now I am trying several in-situ biological techniques and electrical resistance heating also. Depending on where the contamination is, excavation may be the answer with disposal at an appropriate landfill.
I would recommend discussing the site with someone more experienced in environmental remediation, if you don't know anyone locally I'll try to check back on a more regular basis and would be happy to help.
If you have time and room you may consider exsitu bioremediation (windrows for example). Essentially adding nutrients and oxygen to the soil to get the microbes going, then standing back and claiming the credit.
Dual phase vapour extration or air sparging also sound like possibilites dependent upon you site constraints.
What do the governing regs say? Is it leaving the site? Does it pose a risk to the ground / surface water? Does the governing body deem it cost effective to have it remediated? Often times they will sign off on these if it is small, there is no risk of migration, there is no change in land use, etc.