Convergence Issue with 2nd order MUSCL on a hypersonic blunt-body case in SU2

[Smudge-bond]

I have a Laminar Mach 5 Navier-Stokes case over a 2D cylinder-wedge(R=0.1 and 5deg wedge angle) . 1st-order MUSCL converges cleanly (density to -15, energy to -10, matches theory). Switching to 2nd-order MUSCL causes RMS_ENERGY to stall or oscillate between -1 to 1 while density/momentum keep are in the order of -3 to -5.

What I tried:

• Limiter coefficient tuning — VENKAT_LIMITER_COEFF swept from 0.0025 (SU2 default is 0.05) up through 0.03–0.1.
• RAMP_MUSCL to blend gradually from 1st to 2nd order over 8000 iterations in steps of 50, keeping the CFL in range of 0.01 to 0.005 for stability
• LIMITER_ITER diverged the solution when applied
• Flux function swaps from HLLC → AUSM → AUSMPLUSUP2. Nothing changed much about the stability and convergence
• CFL sensitivity was checked and solution was allowed to converged first with low CFL (0.01 to 0.95) with explicit and then with implicit for 1-50 for 1st order. All of the solutions were stable for 1st order muscl.
• Drag coefficient was also observed and was seen flat even while RMS_ENERGY oscillated for 2nd order.

I ran more than 25 cases with different fineness mesh of structured and unstructured grid and each one of them had issues with 2nd order muscl. I would really appreciate some help because I am out of ideas trying to troubleshoot this.
Here is one of the config files:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% SU2 configuration file %
% Case description: VISCOUS flow over a curved wedge %
% Author: %
% Institution: %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
%
SOLVER= NAVIER_STOKES
KIND_TURB_MODEL= NONE
MATH_PROBLEM= DIRECT
VISCOSITY_MODEL=SUTHERLAND
FLUID_MODEL=STANDARD_AIR

%-------------- RESTART SOLUTION --------------------------->
RESTART_SOL=NO
READ_BINARY_RESTART=NO

% -------------------- COMPRESSIBLE FREE-STREAM DEFINITION --------------------%
%
MACH_NUMBER= 5.0
AOA= 0.0
SIDESLIP_ANGLE= 0.0
FREESTREAM_TEMPERATURE= 250.
FREESTREAM_PRESSURE=7.1775E2
FREESTREAM_DENSITY=1E-2
REYNOLDS_NUMBER= 1E6
REYNOLDS_LENGTH= 1.

% ---------------------- REFERENCE VALUE DEFINITION ---------------------------%
%
REF_ORIGIN_MOMENT_X = 0.00
REF_ORIGIN_MOMENT_Y = 0.00
REF_ORIGIN_MOMENT_Z = 0.00
REF_LENGTH= 1.0
REF_AREA= 1.0

% -------------------- BOUNDARY CONDITION DEFINITION --------------------------%
%
MARKER_HEATFLUX=( Nose, 0.0, Wedge,0.0)
%MARKER_FAR= (Inlet, Outlet)
MARKER_SUPERSONIC_INLET=(Inlet,250.,7.1775E2, 1584.7,0.0,0.0)
MARKER_SYM = (Symmetry)
MARKER_OUTLET= (Outlet, 7.1775E2)
MARKER_PLOTTING= ( Nose, Wedge )
MARKER_MONITORING= ( Nose, Wedge )

% ------------- COMMON PARAMETERS DEFINING THE NUMERICAL METHOD ---------------%
NUM_METHOD_GRAD= WEIGHTED_LEAST_SQUARES
CFL_NUMBER= 0.005
CFL_ADAPT= YES
CFL_ADAPT_PARAM=(0.5,1.05,0.005,5)

% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
%
LINEAR_SOLVER= FGMRES
LINEAR_SOLVER_PREC=ILU
LINEAR_SOLVER_ILU_FILL_IN= 1
LINEAR_SOLVER_ERROR= 1.0E-06
LINEAR_SOLVER_ITER= 20

% -------------------- FLOW NUMERICAL METHOD DEFINITION -----------------------%
%
CONV_NUM_METHOD_FLOW= HLLC
MUSCL_FLOW= YES
RAMP_MUSCL= YES
RAMP_MUSCL_COEFF= (30000, 20, 8000)
SLOPE_LIMITER_FLOW= VENKATAKRISHNAN_WANG
%SLOPE_LIMITER_FLOW=VAN_ALBADA_EDGE
VENKAT_LIMITER_COEFF=0.005
TIME_DISCRE_FLOW= EULER_IMPLICIT
%MGLEVEL=0
% --------------------------- CONVERGENCE PARAMETERS --------------------------%
%
CONV_FIELD= RMS_ENERGY
CONV_RESIDUAL_MINVAL= -18
CONV_STARTITER= 500
ITER= 1000000

% ------------------------- INPUT/OUTPUT INFORMATION --------------------------%
%
MESH_FILENAME= M5_unstruc_Hemi_Wedge_5deg_first_y_1e-4_opt2.su2
MESH_FORMAT= SU2
SOLUTION_FILENAME=restart_flow
TABULAR_FORMAT= CSV
RESTART_FILENAME= restart_flow
RESTART_ADJ_FILENAME= restart_adj
GRAD_OBJFUNC_FILENAME= of_grad
OUTPUT_WRT_FREQ= 250
%WRT_SOL_FREQ=250
OUTPUT_FILES=(PARAVIEW,SURFACE_PARAVIEW,RESTART_ASCII)
SCREEN_OUTPUT=(INNER_ITER,RMS_DENSITY,RMS_ENERGY,CFL_NUMBER,DRAG)