Alright, the solution was as simple as attaching the appropriate name onto the HTML DOM element. The final HTML ended up looking something like this:
<div class="form_section" ID="Exhibitors" style="display:none;">
<div class='wExhibitor' data-bind="foreach: $root.exhibitors">
<h2>Exhibitor <span data-bind="text: $index() + 1"></span> Information</h2>
<div class="eccform_section">
<div class="eccform_column">
<div class="eccform_label">First Name*</div>
<div class="eccform_field"><input id="exFirstName" runat="server" class="exFirstName" title="First Name" data-bind="value:FirstName,attr:{name: 'exFirstName_'+$index()}" /></div>
</div>
<div class="eccform_column">
<div class="eccform_label">Last Name*:</div>
<div class="eccform_field"><input id="exLastName" runat="server" class="exLastName" title="Last Name" data-bind="value:LastName, attr:{name: 'exLastName_'+$index()}" /></div>
</div>
</div>
<div class="eccform_section">
<div class="eccform_column_exhibitor">
<div class="eccform_checkbox"><input id="exLunchTicket" name="exLunchTicket" runat="server" type="checkbox" class="exLunchTicket" data-bind="checked: LunchTicket, attr: { name: 'exLunchTicket_' + $index() }">Lunch Ticket ($10)</div>
</div>
<div class="eccform_column_exhibitor">
<div class="eccform_checkbox"><input id="exSeminarTicket" name="exLunchTicket" runat="server" type="checkbox" class="exSeminarTicket" data-bind="checked: SeminarTicket, attr: { name: 'exSeminarTicket_' + $index() }">Seminar Ticket ($40)</div>
</div>
<div class="eccform_column_removebutton">
<button data-bind="click: $root.removeExhibitor">Remove Exhibitor</button>
</div>
</div>
</div>
<button data-bind="click:$root.addExhibitor">Add Exhibitor</button>
</div>
Notice this section:
attr: { name: 'exSeminarTicket_' + $index() }
.
Then, in the C# I corrected the code to look like this:
int SomeKeys = Request.Form.AllKeys.Where(x=>x.StartsWith("exFirstName")).Count();
for (int i = 0; i < SomeKeys; i++)
{
string FirstName = Request.Form["exFirstName_" + i];
string LastName = Request.Form["exLastName_" + i];
bool LunchTicket = Convert.ToBoolean(Request.Form["exLunchTicket_" + i]);
bool SeminarTicket = Convert.ToBoolean(Request.Form["exSeminarTicket_" + i]);
if (FirstName != "" && LastName != "")
lFamilyMembers.Add(new FamilyMember(FirstName, LastName, SeminarTicket, LunchTicket, AgeGroup.Twenties, FamilyRole.Exhibitor));
}