Can you say Shma lying down?

The gemara in Brachos 13b says that, at least for the first few psukim, you need to stand when saying Krias shma. Tosafos (d"h al) asks from the gemara on 11a that Beis Hillel says there that you can say shma whether you're sitting, standing, walking, doing work, or lying down. Tosafos answers that our gemara doesn't mean that you need to stand up, it just means that if you're walking then you should stop and just stand still. Even though Beis Hillel says that meikar hadin you can say Shma while walking it's still better for kavana to be standing still therefore you should do that l'chatchila.

Tosafos does not ask from the gemara lower down on 13b which says that you cannot say shma when lying down. Rashi explains that this is because you're accepting malchus shamayim and it's not kavod to lie down when you're doing that. Does that contradict what Beis Hillel said on daf 11?

[UPDATE] See comments for an explanation why this question probably isn't really a question. I'm not deleting it (yet) because I'm not sure if it's completely wrong.

1. You can answer the same as Tosafos says for amida. You're yotze the mitzva of krias shma if you say it when lying down but l'chatchila you shouldn't. My problem with that explanation is that Beis Shamai says that lying down is the only option at night. It seems strange that if it's such a gnai to say shma lying down that Beis Shamai would demand you do it that way.
2. Rabeinu Yonah says that on daf 11 when it says to "yateh" it doesn't mean lying down but it means sitting and leaning. The problem I have with that is that Beis Shamai says you should do it that way because it says lashon shchiva in the Torah and Beis Hillel uses the same word as B"S.
3. The Maadanei Yom Tov says that B"H just means that you could say it lying down under certain conditions. Like our gemara says that someone really fat could say it lying down.