Share session between two different (but very similar) TechnicalProfiles

Question

Scenario is that during combined SignIn/SignUp flow I'm using following TechnicalProfile for signing in the user with local account:

Base.xml

<TechnicalProfile Id="SelfAsserted-LocalAccountSignin-Email">
    <DisplayName>Local Account Signin</DisplayName>
    <Protocol Name="Proprietary" Handler="Web.TPEngine.Providers.SelfAssertedAttributeProvider, Web.TPEngine, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null" />
    <Metadata>
        <Item Key="SignUpTarget">SignUpWithLogonEmailExchange</Item>
        <Item Key="setting.operatingMode">Email</Item>
        <Item Key="ContentDefinitionReferenceId">api.signuporsignin</Item>
    </Metadata>
    <IncludeInSso>false</IncludeInSso>
    <InputClaims>
        <InputClaim ClaimTypeReferenceId="signInName" />
    </InputClaims>
    <OutputClaims>
        <OutputClaim ClaimTypeReferenceId="signInName" Required="true" />
        <OutputClaim ClaimTypeReferenceId="password" Required="true" />
        <OutputClaim ClaimTypeReferenceId="objectId" />
        <OutputClaim ClaimTypeReferenceId="authenticationSource" />
    </OutputClaims>
    <ValidationTechnicalProfiles>
        <ValidationTechnicalProfile ReferenceId="login-NonInteractive" />
    </ValidationTechnicalProfiles>
    <UseTechnicalProfileForSessionManagement ReferenceId="SM-AAD" />
</TechnicalProfile>

Extensions:

<TechnicalProfile Id="SelfAsserted-LocalAccountSignin-Email">
    <Metadata>
        <Item Key="setting.forgotPasswordLinkOverride">ForgotPasswordExchange</Item>
    </Metadata>
</TechnicalProfile>

Base.xml is taken from one of the starter-packs available on GitHub.

This is working fine and when I'm logged in and go to combined SignUp/SignIn policy again, I'm authenticated automatically without needing to provide any credentials or to select external IdP.

Now, for some other flows (ProfileEdit, PasswordChange) I've slightly modified SelfAsserted-LocalAccountSignin-Email technical profile to not show SignUp/ForgotPassword links.

Technical profile definition:

<TechnicalProfile Id="SelfAsserted-LocalAccountSigninOnly-Email">
    <DisplayName>Local Account Signin</DisplayName>
    <Protocol Name="Proprietary" Handler="Web.TPEngine.Providers.SelfAssertedAttributeProvider, Web.TPEngine, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null" />
    <Metadata>
        <Item Key="setting.showSignupLink">False</Item>
        <Item Key="setting.forgotPasswordLinkLocation">none</Item>
    </Metadata>
    <IncludeTechnicalProfile ReferenceId="SelfAsserted-LocalAccountSignin-Email" />
</TechnicalProfile>

As you can see, it includes the SelfAsserted-LocalAccountSignin-Email and just overrides two setting values.

However, now when the user is authenticated after executing combined SignUp/SignIn policy and he goes to my ProfileEdit policy, he is prompted to authenticate again.

This happens only if user was authenticated using local account, as in my case SignUp/SignIn & ProfileEdit/PasswordChange policies are using different (but very similar) SelfAsserted technical profiles. If user was authenticated using any social idp, ProfileEdit/PasswordChange policies work fine without prompting user for reauthentication.

Any ideas how to solve the issue for the local account?

One solution would be to use the same technical profile for combined SignUp/SignIn and ProfileEdit/PasswordChange and then hide links where necessary using JavaScript, however, if possible I would like to minimize changes made by JS.