|I don't know what CP with 35K time and experienced on radials would tell you not to use carb heat in a DHC-2. If you're talking water then you must be on the coast and particularly at this time of year (and every time of year) you should be expecting carb ice ALL THE TIME. If you're not on the coast, the previous still applies. I hope it isn't the same CP that tells his pilots the DHC-2 burns 15gph and that you should plan your payload accordingly. If it is, that pilot has a history of running low on fuel, and the management of carb heat isn't going to be your only point of disagreement if you're even half a professional.
From the scenario you described, you are very lucky you didn't have an unfortunate incident or accident. Carb air gages are notoriously inaccurate, and even more so when the company considers them unimportant. The MP trick described above is one solution, bearing in mind that every engine and every installation is different. One thing is for sure, definitely apply (smoothly, and over suitable landing areas) bouts of full carb heat regularly in cruise on steamy/misty days, and check on final - check immediately before take-off too.
As an aside, there are no such thing as book fuel consumption anymore for the DHC-2. If you read the manual very carefully you will note that fuel consumption is based on cruise performance with an engine installation equipped with an autolean carburettor, and as previously stated you will be hard pressed to find such an animal anymore. Also, an engineer told me this summer that when 100LL became the norm, the overhaul shops jetted the 985 carburettors with larger jets to provide extra cooling for the higher octane fuel. The only way to verify this for sure is to check with an overhaul shop, but if you rely on book numbers for fuel, you WILL run out of gas. In a radial, the only time you can have too much fuel is when you're on fire.
In a radial, carb ice is your nemesis, is always with you, and is right up there on the list of critical engine handling parameters.
Good on you for asking, however the following is my advice to you: Read the flight manual, read the maintenance manual, and ask credible, experienced operators and mechanics - preferably any you can find on a non-anonymous basis (ie elsewhere than on this forum). On here, you just never know who you're talking to, and those that come across as the most experienced might not reflect reality. If you're ever in the vicinity of an overhaul shop, you can get good tips for engine handling there too.