I would go with the chemical spray/ground treatment around the perimeter as well as the infected wood and do your own inspection (instead of them) and look especially where you've already found them and adjoining spaces.
A good spray/ground treatment should hopefully get them and protect for about 5 years. The cost of the inspection would not include further treatment if any were found so save that part and do your own. While it should last 5 years there is no guarantee that they might be back sooner and on the other hand you may get this one treatment and not see them again for 5, 10, or more years depending upon the conditions around the house like Jay mentioned. Termites are migratory in the ground and each spring they go looking around for food sources. There may be enough residual in the treatment to last a long time depending upon the conditions and ground.
I assume by spray that you mean a ground treatment where they use a 6" trench around the foundation or use a drill/pump and either of which method would put in at least a couple hundred gallons of chemical mix around the foundation that can soak deep into the soil. You also want to spray any wood where the actual infestation is as well as nearby.
The one flaw to your consideration of catching the damage is basically that you need to treat to catch the damage "now" and doing no treatment will mean they are still there and you will catch them again on your next inspection which still means treatment but have another year's worth of damage and make the house that much harder to sell later on. A relative of mine is ordering some chemical today through an internet connection to do their own house. A few hundred dollars worth of chemical and a day's labor should do it. Of course it is legal in my state to do your own. The chemical company knows which states allow chemical to be shipped to unlicensed people.
What is the square footage of your house and the circumference around the house including concrete porches? Also hardwood, softwood, etc. all contain the fibers that make good chewing for termites. Hardwood is just more expensive to replace when damaged.