This same toilet with an insulated tank is SKU CST743SD. It can be found here
Yes, the SoftClose seat for the round front Drake is a model SS113.
here is the spec sheet for this toilet. I do not have the measurement without the lid, however, with the lid, it is 28.5" high.
The CST743S round toilet is only available in the regular bowl height of 14 5/8".