I'd like to offer an alternative view-- especially since you seem to be relatively informed about the more common types of oral lesions.
The fact is that the lesions on your palate are too early in their stage of development to determine whether they are HPV (human papilloma virus) related lesions based on appearance alone. In the mouth, the most common HPV lesion is more properly called a "squamous papilloma" rather than a wart, but for purposes of discussion it need not matter.
The more salient points follow. First: a papilloma needs to mature a bit before it displays its more characteristic appearance, and your lesions have not yet reached that stage. It is true, however, that the posterior hard palate and soft palate are common sites for papilloma.
There are perhaps over 100 different strains of HPV, and the various strains show a predilection for different anatomic areas and tissues. The most important strain in terms of health significance is HPV-16, which is associated with cancers in the mouth, oropharynx, genitalia, and vaginal cervix. Having said that, HPV-16 is also associated with non-cancerous lesions, so the factors that determine the type of lesion it may cause may be related to host physiology in addition to serotype characteristics of the virus.
Because a majority of squamous papillomas are relatively trivial, they are not always treated aggressively. Likewise, an early lesion that may suggest HPV (as yours may) will not necessarily call for active intervention, although there is some variance in how a particular clinician will treat this. Unlike viruses in the herpesvirus group (e.g., HSV, VZV, EBV, or CMV), HPV is not recognized to cause a persistent infection, and most patients with normal immunity will clear the virus within a year or two.
Just what you do going forward should be decided by a collaborative discussion with your dentist. Most general dentists will refer their patients to an oral surgeon for more formal evaluation, because this specialist will have more familiarity with soft tissue lesions. The only definitive way to identify these lesions, particularly at this early stage, would be biopsy. Your oral surgeon may instead choose to simply keep the lesions under active surveillance, and deferring any decision regarding removal until the clinical behavior of these lesions can be more completely observed.
Hope this helps...