I think texting H a "good morning" or "have a great day" message is perfectly fine and even a good idea. If you have no expectations about it - as in, you won't fall to pieces if he doesn't reciprocate - then this practice (once in a while, especially while H is home and not, to your knowledge, in an active A) is a good-faith effort on your part to be friendly (albeit a tad more-than-neighborly) even when you're getting the cold shoulder. It also is an ACTION that will be good practice for YOU to bust through your own awkward feelings and to try to stay light and breezy toward H. In other words, it'll help keep you from showing your true negative feelings. Grace under fire. Again.
Like JCred said: maybe try it for a couple weeks and monitor results. If it doesn't help after you are consistent, switch it up.
Meanwhile, sweet girl, what are you doing for YOU? If your H isn't telling you his whereabouts and is coming home whenever, you really need to get out of the house some yourself. I know your work schedule is brutal. But a night out should be on tap really, really soon. A walk. A new outfit. Some new make-up. A new body spray/perfume. Don't you need a manicure or something? A new hair-cut or color? Some new lingerie that you - whoops - accidentally walk out of the bathroom in (in front of H) after a long, hot shower and a spray of that new fragrance??
Please go get your groove back. For YOU. Those changes are supposed to be forever. Forever. Not just to win back H. And you KNOW how much better you'll start feeling about yourself. It will help so much. This isn't to get back at H or to make him take notice. This is to help YOU. And usually? He's gonna notice. But that's an unintended "benefit."
M: 40 H: 44 Married 14 years S11 & D6; D20 & D19 from previous M 2BDs/PAs, 8 years apart Piecing: April 2014