Yes but not in the game. The option is switchable in the Map Editor(Galaxy Forge) therefore only applies to a particular map. You can easily open a existing map set the option to off and save the map as a custom map. Then the first cap will be full price.

How would I go about doing that? I have played around with Entity files but never added an entirely new one. I was thinking maybe add it in as a tier 2 combat technology.

Adding a new tech is quite a lot of work if you want to do it properly. Lets start with the shipyards(e.g. PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY.entity): Just add the bold part to the file. As you already have a Cap factory when you select quick start it is not working then. If it is supposed to work for quick start as well you have to add this prerequesite to every Capship, too.

TXT
entityType "PlanetModuleShipFactory"
minZoomDistanceMult 1.000000
ability:0 "AbilityProtectedShutdown"
ability:1 ""
ability:2 ""
ability:3 ""
MaxAntiMatter 0.000000
AntiMatterRestoreRate 0.000000
numRandomDebrisLarge 3
numRandomDebrisSmall 18
numSpecificDebris 0
armorType "VeryHeavy"
hudIcon "HUDICON_PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY"
smallHudIcon "HUDICONSMALL_PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY"
infoCardIcon "INFOCARDICON_PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY"
planetUpgradeSlotType "Civilian"
planetUpgradeSlotCount 4.000000
basePrice
    credits 1000.000000
    metal 250.000000
    crystal 100.000000
BuildTime 60.000000
NameStringID "IDS_PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY_NAME"
DescriptionStringID "IDS_PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY_DESCRIPTION"
planetModuleRoleType "CAPITALSHIPFACTORY"
statCountType "ModuleCapitalShipFactory"
Prerequisites
    NumResearchPrerequisites 1
    ResearchPrerequisite
        Subject "RESEARCHSUBJECT_PLANETMODULEACCESS_PHASECAPSHIPYARD"
        Level 1
MaxHullPoints 4500.000000
HullPointRestoreRate 2.000000
BaseArmorPoints 6.000000
MaxShieldPoints 0.000000
ShieldPointRestoreRate 0.000000
maxShieldMitigation 0.000000
ExperiencePointsForDestroying 25.000000
angularSpeed 0.000000
rotateSoundName ""
resourceExtractionType "Invalid"
cultureSpreadRate 0.000000
rotateToFacePlanet FALSE
rotateConstantly FALSE
isAffectedBySimilarModuleCostResearch FALSE
ShieldMeshName ""
NumSoundsFor:ONATTACKORDERISSUED 0
NumSoundsFor:ONCREATION 0
NumSoundsFor:ONGENERALORDERISSUED 0
NumSoundsFor:ONSELECTED 1
SoundID "PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY_ONSELECTION_0"
NumSoundsFor:ONSTARTPHASEJUMP 0
MeshName "PlanetModule_PhaseOrbitalCapitalShipFactory"
ExplosionName "PlanetModuleLarge"
mainViewIcon "MAINVIEWICON_PLANETMODULE_PHASEORBITALCAPITALSHIPFACTORY"
picture "PLANETMODULEPICTURE_PHASEORBITALCAPITALSHIPFACTORY"
minShadow 0.000000
maxShadow 1.000000
formationRank 3

You have to do this for all 3 fractions with different technology names of course.

Then you have to make 3 new tech files: (here: RESEARCHSUBJECT_PLANETMODULEACCESS_PHASECAPSHIPYARD.entity)

TXT
entityType "ResearchSubject"
hudIcon "HUDICON_CAPITALSHIP_PHASEBATTLESHIP"
smallHudIcon "HUDICONSMALL_CAPITALSHIP_PHASEBATTLESHIP"
infoCardIcon ""
NameStringID "IDS_RESEARCHSUBJECT_FRIGATEACCESS_PLANETMODULEACCESS_PHASECAPSHIPYARD_Info"
DescriptionStringID "IDS_RESEARCHSUBJECT_FRIGATEACCESS_PLANETMODULEACCESS_PHASECAPSHIPYARD_Description"
researchWindowLocation
    block 0
    pos [ 0 , 0 ]
ResearchField "Combat"
Prerequisites
    NumResearchPrerequisites 0
MinimumArtifactLevel -1
BaseUpgradeTime 45.000000
PerLevelUpgradeTime 5.000000
BaseCost
    credits 600.000000
    metal 50.000000
    crystal 100.000000
PerLevelCostIncrease
    credits 100.000000
    metal 25.000000
    crystal 25.000000
Tier 1
onlyWorksIfTierLabsExist TRUE
MaxNumResearchLevels 1
priority 0.000000
researchBoolModifiers 0
researchFloatModifiers 0
artifactPicture ""

The researchWindowLocation must be a free spot in the research window. if counts from the top and from left, starting at 0. So
Block 1
pos[ 0 , 2 ]
is the second tab, first row, third line

Again do this for all fractions. I don't want to explain how to make icons so i just used the ones from the vasari battleship.

Now you need to write the research description.

Write it down in the text editor in the following pattern:

StringInfo
    ID "IDS_RESEARCHSUBJECT_FRIGATEACCESS_PLANETMODULEACCESS_PHASECAPSHIPYARD_Info"
    Value "Your Description"
StringInfo
    ID "IDS_RESEARCHSUBJECT_FRIGATEACCESS_PLANETMODULEACCESS_PHASECAPSHIPYARD_Description"
    Value "Your Description"

When you are finished copy it and paste it at the end of the english.str (Or your language). You have to increase the counter at the beginning of the file(NumStrings XXXX), so Sins can find the strings. In Your case you have to add 6.

Finally you have to make the tech reseachable for the fractions. Open the player files (e.g. PlayerPhase.entity)

there you will find this part:

    researchInfo
        count 119
        entityDefName "RESEARCHSUBJECT_ABILITYACCESS_CLUSTERWARHEADS"
.
.
.

       entityDefName "RESEARCHSUBJECT_PLANETMODULEACCESS_PHASECAPSHIPYARD"

Add the tech for that race, increase the counter, save it and use harpos99999's manifest maker to...well to make a manifest (only entity).

Then it should work. You can have a look at this mod. It adds a few reseach subjects as well.