= Solution
<Chandrasekhar dynamical friction> is the drag exerted by the overdense gravitational wake that a massive body creates in a background of lighter particles. It transfers orbital energy and <angular momentum> to the host, causing satellites, star clusters, and massive black holes to spiral inward and promoting galaxy mergers. In a homogeneous isotropic Maxwellian background its force is
$$
\mathbf F_{\rm df}=-4\pi G^2M^2\rho\log\Lambda
\left[\operatorname{erf}(X)-\frac{2X}{\sqrt\pi}e^{-X^2}\right]
\frac{\mathbf v}{v^3},
\qquad X=\frac{v}{\sqrt2\sigma},
$$
where $\log\Lambda$ is the <Coulomb logarithm in stellar dynamics>. Its scaling can be reconstructed from the strong-deflection <impact parameter> $b_{\rm cr}\sim GM/v^2$: the encountered mass rate is $\sim\rho v\pi b_{\rm cr}^2$, and multiplying by momentum change $\sim v$ gives $F_{\rm df}\sim G^2M^2\rho/v^2$.
For a spherical host with a <flat galaxy rotation curve>,
$$
M_h(<r)=\frac{v_c^2r}{G},
\qquad
\rho_h(r)=\frac{v_c^2}{4\pi Gr^2}.
$$
This is a <singular isothermal sphere> with one-dimensional dispersion $\sigma=v_c/\sqrt2$, so $X=1$. Define
$$
C=\operatorname{erf}(1)-\frac{2e^{-1}}{\sqrt\pi}\simeq0.428.
$$
For a constant-mass satellite on a <circular orbit>, the drag magnitude and its <torque> are
$$
F_{\rm df}=\frac{CGM_s^2\log\Lambda}{r^2},
\qquad
\frac{d}{dt}(M_sv_cr)=-rF_{\rm df}.
$$
It follows that
$$
\dot r=-\frac{CGM_s\log\Lambda}{v_cr},
\qquad
\boxed{t_{\rm df,0}=\frac{v_cr_0^2}{2CGM_s\log\Lambda}
\simeq\frac{1.17v_cr_0^2}{GM_s\log\Lambda}}.
$$
The quadratic radius dependence and inverse mass dependence explain why massive nearby satellites merge much faster than light or distant ones.
Let the satellite also have a flat internal rotation curve of speed $v_s$. Equating its edge density to the host density gives the <tidal radius>
$$
\frac{v_s^2}{4\pi GR_t^2}=\frac{v_c^2}{4\pi Gr^2},
\qquad
R_t(r)=\frac{v_s}{v_c}r.
$$
Because $M_s(\lt R_t)=v_s^2R_t/G$, the bound mass decreases linearly:
$$
M_s(r)=M_s(r_0)\frac r{r_0}.
$$
Under the question's literal closure that the <derivative> of the remaining satellite's total orbital angular momentum equals the frictional torque,
$$
\frac d{dt}\left[M_s(r)v_cr\right]
=-\frac{CGM_s(r)^2\log\Lambda}{r},
$$
and hence
$$
\dot r=-\frac{CGM_s(r_0)\log\Lambda}{2v_cr_0},
\qquad
\boxed{t_{\rm df,strip}=\frac{2v_cr_0^2}{CGM_s(r_0)\log\Lambda}=4t_{\rm df,0}}.
$$
If stripped material is explicitly assigned the satellite's instantaneous specific orbital angular momentum, the balance for the bound remnant is instead $M_s\,d(v_cr)/dt=-rF_{\rm df}$; that convention gives $t_{\rm df,strip}=2t_{\rm df,0}$. Both treatments show the robust point: <tidal stripping> weakens the drag as the orbit shrinks and substantially delays coalescence. In less idealized profiles the mass can fall faster than linearly, producing <dynamical-friction stalling by tidal stripping>.
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