No, that will NOT work - it's a common misconception. The 5-lnb and 3-lnb LNBs themselves (non-SWM) are electrically different. If you have a 5-lnb dish and then tell the receiver you only have a 3-lnb, the receiver won't look for 110/119 BUT when you are tuned to a channel on 103 the guide data still only comes from 119, so you won't get guide data. The slimline 3LNB takes the guide data from 101, and puts it on the lines from the dish so the receiver still sees it when tuned to a 103 transponder.
SWM LNBs (SL5 or SL3) only take the guide data from 101 so there's no issue with lack of line of sight to 119.
If you call DirecTV for service (free with the protection plan, $50 otherwise)and tell the CSR you are having problems with low signals, the tech will replace the dish with a slimline, an SL5 if you are in an area that gets SD locals from 119, an SL3 otherwise. But he won't necessarily use an SWM dish, you might be able to "persuade" him to do that. Of course, if you have other receivers that are not SWM compatible that's a non-starter. And if you are in an area that gets SD locals from 119 (you didn't give us your zip code) the tech probably won't have an SL3 on the truck, only an SL5.
If you are in an area getting SD locals from 119, your only way to get an SL3 (and thereby not get any SD locals) is to buy it yourself - several eBay vendors can give you this at a good price (don't forget with the SWM dish you will need a power inserter).