Fascinating study. I hope this can be start of a discussion on how to improve our crucial immunity when this is poor.
Unfortunately the optimized protocol of the study linked by John that achieved in depleting my-HSCs in mice cannot be used by us now. It achieved this by targeting the CD62p antigen using an anti-CD62p antibody of mouse lgG2a isotope in combination with NEO1 antigen using combined goat anti-mouse NE01 antisera with anti-CD47 and anti-KIT. Anyone care to ask the researchers to supply those substances with dosage recommendations 
Another possible way to deplete my-HSC is by addressing changes in the bone marrow microenvironment, from a study focused on leukemia: . Hematopoietic stem cell aging and leukemia transformation | Blood | American Society of Hematology (ashpublications.org) In this study, a more complicated and much broader range of HSC deficiencies are described than just myeloid bias : “old HSCs have impaired hematopoiesis,[3] myeloid bias at the transcriptome and functional levels,[4]( dysfunctional mitochondria,[5]) decreased polarity of Cdc42,[6]increased reactive oxygen species (ROSs),[increased γH2.AX caused by ineffective H2.AX dephosphorylation rather than sustained DNA damage,[8]altered DNA methylation,[9](changes in histone modification patterns[10] (which are also observed in aged human hematopoietic stem and progenitor cells [HSPCs]),[11]and increased transformation to leukemia.
The most promising method I could find from this study is on fecal microbiota transplantation: “Fecal microbiota transplantation from young mice into old mice rejuvenated HSC function, mitigated inflammatory signaling, and restored lymphoid differentiation capacity of aging HSCs”… … “Autologous fecal microbiota transfer has been shown to be safe in patients with AML in a recent phase 2 clinical trial.[76] These observations supports alterations in gut microbiota and intestinal barrier damage during aging dysregulates HSC function and provides a therapeutic option for restoring HSC function and preventing hematologic malignancies”.
**Fecal transplants were covered in Can Fecal Transplants Help Reverse Aging? Taking resistant staches, sauerkraut and having a veggy-berry heavy diet, I´m not sure I would wind up winning from a fecal transplant and would have to make an analysis of my gut bacteria first.
Pharmacological inhibition of interleukin 1β (IL-1β) (reduces inflammation, probably not an issue for most on this forum) and senolytics are amongst the other potential methods described for reducing my-HSCs.
In my own case, most important is to increase lymphocytes, that are an abysmally low 0.6 (ref range 1.1-3.5) despite doing everything right in life-style factors (possibly a long-lasting result of radiation therapy over 3 years ago), rather than improving the neutrophil(myeloid)/lymphocyte ratio which at 3 is not good but not disastrous.
Searching, I find that lithium increases white blood cell count perhaps from action in the bone marrow. However the effect is dose-dependent and it was for bi-polar patients so with the low-lithium dose many of use it may not be relevant. The effects of lithium therapy on leukocytes: a 1-year follow-up study. - PMC (nih.gov)
Finally, there are pharmacological interventions e.g. Targeted Drug Delivery to Lymphocytes: A Route to Site-Specific Immunomodulation? | Molecular Pharmaceutics (acs.org) Fairly heavy stuff, have not checked it.