As already asked - do you really care about the lost energy? Cost wise it's not liable to matter. Thermally it may.
You can easily enough achieve what you want, not by switching between supplies but instead by adding in a second supply when required. Your acceptable response time of "several hundred milliseconds" is 10+ whole mains cycles so (assuming this is mains powered), so response time from a "standing start" should be easily enough achievable.
You could feed the second supply to the load via a diode to allow it to be turned on and off "somewhat gracefully". You don't say how precise you need the voltage to be but with proper design you should be able to achieve "take up" by the larger supply as the smaller supply droops somewhat or have the voltage rise 'just slightly' as the large supply cuts in.
If you don't mind a relatively minor piece of custom electronics then a custom regulator and switch would be relatively easy to implement. Large supply can then be able to make somewhat more voltage than needed at say 2A and the regulator/switch drops the voltage difference to ensure that the 30V output is maintained.
This could almost be done with just a linear regulator (eg LM350) and a diode but the regulation would be imperfect (maybe a few tenths of a volt variation across zero to full load due to the LM350 voltage sense being somewhat decouples behind the output diode). Adding a single opamp section and a low cost voltage reference would allow the 30V rail to be maintained "rock steady" once the large supply had reached design output level.
BUT! - your bricks have an unacceptably bad no load rating. Modern supplies are able to do far better than what you are quoting. Wattages under 1 Watt idle are typical for supply designs targeted at consumer appliances where standby power is now considered a major issue. (Rule of thumb: 1 watt always on typically costs ~~= $2/year - obviously depending on your power charges)
As has been noted, you can certainly buy supplies that come much closer to what you want than what you have now. BUT the admitted 'kluge' of a custom off the shelf supply optimised for very high efficiency at say 150-300 mA plus a custom "pick up the load" system would allow a very quick and easy and overall very efficient system. If you do this you MUST ensure that the large supply is never required during normal operation. ie if the low Wattage supply can supply up to 300 mA at acceptable voltage, normal operation MUST NEVER exceed 300 mA or the large supply will be cutting in and out semi randomly. The custom large wattage supply needs some means of detecting the need for high current and switching in for a finite period. This could be based on droop of the small system under load or by the test system providing a "wakeup" signal. An off the shelf power supply may be available to do this but the requirement is specialised enough (even though simple) that making your own is probably preferred if the capability is available.