For starters, deadlifting properly (in a technical sense) involves neither tapping the ground nor nearly tapping the ground with the weight. It is a full stop between reps. However, in your case, this may not be what's best.
There are several options that you can make use of.
If you have access to bumper plates, then consider using these, as each plate is the same diameter as a 45 lb plate.
If bumper plates are not an option, consider a deadlift variation. In your case, I would recommend a Romanian deadlift. This starts at the top and only goes as low as your neutral back will allow. Stiff-legged deadlifts (SLDLs) are another option, which also start at the floor but the knees experience very little flexion or extension during the lift. However, the SLDL is a bit more technical and can set you up with bad habits for when you get back to normal deadlifts.
Another option is to do block pulls or rack pulls which will raise the bar to a more comfortable height. This will, however, shift the focus more towards your back (not necessarily a bad thing, just something to keep in mind).
Pulling in a sumo stance may be another option that might work for you. Due to the angles of your legs in this stance, there is relatively less knee bend while doing sumo deadlifts than conventional deadlifts. Granted, more hip mobility is required for this stance than a conventional deadlift.
If none of these work well enough for you, then perhaps revisiting deadlifts after you have lost some more weight or can tolerate the necessary mobility will be better.
As a final note, deadlifts don't have a requisite height, rather they simply become relatively easier as the bar starts at a higher position relative to the ground. It's common to start with a 45 on either side, as that's the highest a standard deadlift will get as the weight goes up. A lot of lifters don't want to constantly mess around with changing from smaller to larger plates for warming up, so starting with 45's is a decent compromise (and as one gets stronger 135 becomes a valid weight for starting one's warm-up). There is nothing wrong with starting with a light deadlift that sits lower than a standard deadlift (with 45's) and then working up in weight (even if that too is lower).