I'll tell you this, if you wanna use a weed razor, you'd better have arms like Popeye. The only good thing about mechanical removal goes inline with how you think its coming in with the geese. Elodea grows best in high light, high nutrient waters so removing the plant (as much as you can) will bit by bit remove nutrients from the lake. I agree with JHAP, knocking it down 20% at a time with cutrine/reward will kill it but the nutrients will stay in the water providing food for the next batch when the geese bring it in. Also, if it has grown uncontrolled for even one season, you're gonna have buds and seeds resting on the bottom. Best case scenario, combine the two methods like we do here with Lake Mowers. Cut it to remove the bulk of the mass, then treat the remaining to knock out any cuttings or immature plants. Floating seine nets work at controlling the spreading of cuttings so you can work on an area with out it spreading to finished areas.
Sorry about being so long winded. Down here in Texas many of the agencies would rather 'maintain' the weed problem rather than 'fix' the problem (cough lake austin cough). It becomes a wonderful source of continued incom...i mean drain on taxpayer money. :P