diff --git a/.github/workflows/test_branches.yml b/.github/workflows/test_branches.yml
index 4e45407e8b2..f6f0277437f 100644
--- a/.github/workflows/test_branches.yml
+++ b/.github/workflows/test_branches.yml
@@ -23,7 +23,7 @@ env:
   PYTHON_CORE_PKGS: wheel
   PYPI_ONLY: z3-solver linear-tree
   PYPY_EXCLUDE: scipy numdifftools seaborn statsmodels linear-tree
-  CACHE_VER: v260512.3
+  CACHE_VER: v260804.0
   NEOS_EMAIL: tests@pyomo.org
   SRC_REF: ${{ github.head_ref || github.ref }}
   PYOMO_WORKFLOW: branch
diff --git a/.github/workflows/test_pr_and_main.yml b/.github/workflows/test_pr_and_main.yml
index f8b8eed355b..64822ed3613 100644
--- a/.github/workflows/test_pr_and_main.yml
+++ b/.github/workflows/test_pr_and_main.yml
@@ -31,7 +31,7 @@ env:
   PYTHON_CORE_PKGS: wheel
   PYPI_ONLY: z3-solver linear-tree
   PYPY_EXCLUDE: scipy numdifftools seaborn statsmodels linear-tree
-  CACHE_VER: v260512.3
+  CACHE_VER: v260804.0
   NEOS_EMAIL: tests@pyomo.org
   SRC_REF: ${{ github.head_ref || github.ref }}
   PYOMO_WORKFLOW: |
@@ -196,7 +196,7 @@ jobs:
           PACKAGES: pyutilib
 
         - os: ubuntu-latest
-          python: 'pypy-3.11-v7.3.20'  #FIXME: Temporary version pin to avoid PyPy 7.3.21
+          python: 'pypy-3.11'
           TARGET: linux
           PYENV: pip
 
diff --git a/pyomo/contrib/satsolver/tests/test_satsolver.py b/pyomo/contrib/satsolver/tests/test_satsolver.py
index 9e92ca23bef..f527019286d 100644
--- a/pyomo/contrib/satsolver/tests/test_satsolver.py
+++ b/pyomo/contrib/satsolver/tests/test_satsolver.py
@@ -32,9 +32,13 @@
 from pyomo.gdp import Disjunct, Disjunction
 
 exdir = join(PYOMO_ROOT_DIR, 'examples', 'gdp')
+from pyomo.common.envvar import is_pypy
 
 
 @unittest.skipUnless(z3_available, "Z3 SAT solver is not available.")
+@unittest.skipIf(
+    is_pypy, "satsolver tests stall on pypy; these will no longer be tested."
+)
 class SatSolverTests(unittest.TestCase):
     def test_simple_sat_model(self):
         m = ConcreteModel()
diff --git a/pyomo/core/tests/unit/test_pickle.py b/pyomo/core/tests/unit/test_pickle.py
index f8cf3ab6ed6..706a3bf0927 100644
--- a/pyomo/core/tests/unit/test_pickle.py
+++ b/pyomo/core/tests/unit/test_pickle.py
@@ -31,8 +31,8 @@
     NonNegativeReals,
     sum_product,
 )
-
-is_pypy = platform.python_implementation().lower().startswith("pypy")
+from pyomo.common.dependencies import dill_available
+from pyomo.common.envvar import is_pypy
 
 
 def obj_rule(model):
@@ -319,7 +319,7 @@ def rule2(model, i):
         model.con = Constraint(rule=rule1)
         model.con2 = Constraint(model.a, rule=rule2)
         instance = model.create_instance()
-        if is_pypy:
+        if is_pypy and dill_available:
             str_ = pickle.dumps(instance)
             tmp_ = pickle.loads(str_)
         else:
diff --git a/pyomo/gdp/tests/test_mbigm.py b/pyomo/gdp/tests/test_mbigm.py
index dfe1aac201b..3f989a8b4a1 100644
--- a/pyomo/gdp/tests/test_mbigm.py
+++ b/pyomo/gdp/tests/test_mbigm.py
@@ -17,6 +17,7 @@
 from pyomo.common.fileutils import import_file, PYOMO_ROOT_DIR
 from pyomo.common.log import LoggingIntercept
 import pyomo.common.unittest as unittest
+from pyomo.common.envvar import is_pypy
 from pyomo.core.expr.compare import (
     assertExpressionsEqual,
     assertExpressionsStructurallyEqual,
@@ -1136,6 +1137,10 @@ def test_calculate_Ms_infeasible_Disjunct(self):
     @unittest.skipUnless(
         SolverFactory('ipopt').available(exception_flag=False), "Ipopt is not available"
     )
+    @unittest.skipIf(
+        is_pypy,
+        "tests using multiprocessing stall on pypy; this will no longer be tested.",
+    )
     def test_calculate_Ms_infeasible_Disjunct_local_solver(self):
         m = self.make_infeasible_disjunct_model()
         # When multiple exceptions are raised during a
diff --git a/pyomo/solvers/plugins/solvers/cuopt_direct.py b/pyomo/solvers/plugins/solvers/cuopt_direct.py
index 4ccdc9e631d..11e8dd6741d 100644
--- a/pyomo/solvers/plugins/solvers/cuopt_direct.py
+++ b/pyomo/solvers/plugins/solvers/cuopt_direct.py
@@ -37,7 +37,11 @@ def _get_cuopt_version(cuopt, avail):
     CUOPTDirect._name = "cuOpt %s.%s%s" % CUOPTDirect._version
 
 
-cuopt, cuopt_available = attempt_import("cuopt", callback=_get_cuopt_version)
+# Note: catch RuntimeError as the base for CUDARuntimeError, which can
+# be raised, e.g., for CUDA driver version mismatches
+cuopt, cuopt_available = attempt_import(
+    "cuopt", callback=_get_cuopt_version, catch_exceptions=(ImportError, RuntimeError)
+)
 
 
 @SolverFactory.register("cuopt", doc="Direct python interface to CUOPT")
diff --git a/pyomo/solvers/tests/checks/test_cuopt_direct.py b/pyomo/solvers/tests/checks/test_cuopt_direct.py
index fa6620a603e..761aab44a56 100644
--- a/pyomo/solvers/tests/checks/test_cuopt_direct.py
+++ b/pyomo/solvers/tests/checks/test_cuopt_direct.py
@@ -24,7 +24,6 @@
     Binary,
 )
 import pytest
-from pyomo.common.dependencies import attempt_import
 from pyomo.opt import check_available_solvers
 from pyomo.common.tee import capture_output
 from pyomo.common.tempfiles import TempfileManager
diff --git a/setup.py b/setup.py
index bcc8af4a666..aecd7e6afbf 100644
--- a/setup.py
+++ b/setup.py
@@ -215,7 +215,6 @@ def __ne__(self, other):
             'scipy',  # Needed by autodoc for pynumero
         ],
         'optional': [
-            'dill',  # No direct use, but improves lambda pickle
             'ipython',  # contrib.viewer
             'linear-tree; python_version<"3.14"',  # contrib.piecewise
             # FIXME: This is a temporary pin that should be removed
@@ -253,6 +252,7 @@ def __ne__(self, other):
             # install on PyPy (binary wheels are not available), so we
             # will only "require" them on other (CPython) platforms:
             'casadi; implementation_name!="pypy"',  # dae
+            'dill; implementation_name!="pypy"',  # No direct use, but improves lambda pickle
             'numdifftools; implementation_name!="pypy"',  # pynumero
             'pandas; implementation_name!="pypy"',
             'seaborn; implementation_name!="pypy"',  # parmest.graphics