She sounds very much like the youngest of my three deaf dogs, [ mine are all collie`s but until she passed away I also had a deaf lad x poodle ]. Your dog sounds to have very similar behaviours to my youngest, particularly regarding the almost obsessive nose on the ground.
I worked on her training indoors initially, [ sit, down, close recall ], and once those were consistant I worked on them in the garden next, so that though distractions for sniffing etc were there, it was a safe closed environment. Every time she so much as glanced at me while sniffing around, I used her recall signal and facial expression of a beaming smile, and she soon started coming to me between ground sniffing, gradually watching me more and more and becoming more responsive to recall then her other basics outside despite distractions.
I would do a brief session on those then let her sniff around again uninterupted for a few minutes, then do another brief session and so on, gradually building up the time she was able to focus and concentrate.
I then introduced using her favourite toys which has resulted in the makings of excellent recall for the time I feel she is ready to be able to go off lead in unfamiliar areas later on.
When on lead away from her familiar surroundings, I let her have free reign to have her head down, on a long training lead not a short one, and never forcing her head up. Again, as with the garden work, I would wait for her to glance at me then would interact and reward with praise, [ visual signal ], and food reward.
Over a relatively short period of time, because I gave her the opportunity to seek interaction from me on walks for which she is rewarded, rather than force it, she now walks pretty much like any other dog, head up and responsive, with occasional sniffs at the ground as all dogs should be able to do, [ its *their* walks after all ].
She is doing agility training at the moment which has come on very well due to the previous base work. I use an outdoor enclosure for her agility so that she is free to safely sniff around and be in her own little world but she is doing that less and less all the rime as she `checks back` so often now and gets a tremendous response from me for it.
I also do `chase me` games, where I walk, jog, and run away from her in different directions, on long line on open ground and off lead altogether in the [ large ] enclosure, so that she watches me more, the idea being to be more interesting to her than anything else, which has improved her focus no end.
If any of the above is something you can try, if there is an enclosed area available, or using a longline on harness [ NEVER to collar or head collar ], so long as you steadily build up the distance as you both get used to a line so that she does`nt get it wrapped around her legs etc, you should find your dog starting to get more responsive.
I would also strongly suggest you check out the website and booklets by Barry Eaton for tips on signals, attention getting, and general info on deaf dogs
http://www.barry.eaton.clara.net/
If you would care to tell me your dogs breed or mix if known, I can consider breed traits which you may be able to use to advantage, [ if your dog exhiits any ], if you are open to suggestions from me.
My eldest deaf dog incidentally, also started fairly similarly to my youngest though not so scent obsessed. He has been competing in agility for many years and has taught me an incredible amount about communication with deaf dogs.
I found the key was to let the dogs guide me as to what visual cues and interactions they find easiest to understand and to use their natural behaviours, especially simple glances at me at any time, toward formal training aspects. [ I will add, I use positive methods only, no force and no punitive punishment - its all reward and fun based methods which I use ].
We tried light, but that had no effect at all! 
