Validation messages across required fields with converter - validation

Question

I have a form with multiple fields, of which I need one of them required to continue or a group of them. For simplicity, I'll just paste a simpler version of my code here
<h:form id="searchForm">
<p:growl for="searchForm" showDetail="true" showSummary="true"/>
<p:inputText id="name"
value="#{backingBean.name}"
required="#{backingBean.nameRequired and backingBean.masterRequired}">
<p:ajax />
</p:inputText>
<h:panelGroup id="dateForm">
<p:inputMask id="date"
value="#{backingBean.date}"
mask="99/99/9999"
required="#{backingBean.dateRequired and backingBean.masterRequired}"
converterMessage="Please insert using format dd/mm/yyyy">
<f:convertDateTime pattern="dd/MM/yyyy" />
<f:validator validatorId="dateValidator" />
<p:ajax update="dateForm" />
</p:inputMask>
</h:panelGroup>
<p:selectOneMenu id="documentType" effect="fade"
value="#{backingBean.documentType}"
required="#{backingBean.documentRequired and backingBean.masterRequired}">
<f:selectItem itemLabel="Select document type" noSelectOption="true" />
<f:selectItems
value="#{constantsController.docType.entrySet()}"
var="entry" itemValue="#{entry.key}" itemLabel="#{entry.value}" />
<p:ajax />
</p:selectOneMenu>
<p:inputText id="documentNumber"
value="#{backingBean.documentNumber}"
required="#{backingBean.documentRequired and backingBean.masterRequired}">
<p:ajax />
</p:inputText>
<p:commandButton id="searchButton"
value="Search"
action="#{controllerBean.submitSearch}"
icon="ui-icon-search">
<p:ajax
listener="#{backingBean.checkRequired()}" update="#form" />
</p:commandButton>
</h:form>
When all fields are empty, the is shown as it should. Now what I need is the inputMask date to only show the converter message and the validation message. I need it to not show the message when the requiredMessage will try to be shown.
I tried putting a <p:message for="date" rendered="#{!empty param['date']}" /> but it does not work, since it is not rendered on the first load, and ajax does not update the panelGroup, I think it is because since I gave an invalid value to the converter, it does not fire the update.
Additional information:
As you can see, I have multiple required fields, I need at least one of these:
-name
-date
-document type + document number
Now, to validate the required fields, I'm doing the following on my backing bean:
public void checkRequired() {
nameRequired = name.equals("");
dateRequired = date == null;
documentRequired = documentType.equals("") || documentNumber.equals("");
masterRequired = nameRequired && dateRequired && documentRequired;
if(masterRequired)
{
FacesMessage message = new FacesMessage(FacesMessage.SEVERITY_WARN, "Incomplete form",
"Please insert at least 1 field");
FacesContext.getCurrentInstance().addMessage("searchForm", message);
return;
}
}